This dissertation develops a computational method for simulating laser-induced cavitation and investigates the mechanism behind the formation of non-spherical bubbles induced by long-pulsed lasers. The proposed computational method accounts for the laser emission and absorption, phase transition, and the dynamics and thermodynamics of a two-phase fluid flow. In this new method, the model combines the Navier-Stokes (NS) equations for a compressible inviscid two-phase fluid flow, a new laser radiation equation, and a novel local thermodynamic model of phase transition. The Navier-Stokes equations are solved using the FInite Volume method with Exact two-phase Riemann solvers (FIVER). Following this method, numerical fluxes across phase boundaries are computed by constructing and solving one-dimensional bi-material Riemann problems. The new laser radiation equation is derived by customizing the radiative transfer equation (RTE) using the special properties of laser, including monochromaticity, directionality, high intensity, and a measurable focusing or diverging angle. An embedded boundary finite volume method is developed to solve the laser radiation equation on the same mesh created for the NS equations. The fluid mesh usually does not resolve the boundary and propagation directions of the laser beam, leading to the challenges of imposing the boundary conditions on the laser domain. To overcome this challenge, ghost nodes outside the laser domain are populated by mirroring and interpolation techniques. The existence and uniqueness of the solution are proved for the two-dimensional case, leveraging the special geometry of the laser domain. The method is up to second-order accuracy, which is also proved, and verified using numerical tests. A method of latent heat reservoir is developed to predict the onset of vaporization, which accounts for the accumulation and release of latent heat. In this work, the localized level set method is employed to track the bubble surface. Furthermore, the continuation of phase transition is possible in laser-induced cavitation problems, especially for long-pulsed lasers. A method of local correction and reinitialization is developed to account for continuous phase transitions. Several numerical tests are presented to verify the convergence of these methods. This multiphase laser-fluid coupled computational model is employed to simulate the formation and expansion of bubbles with different shapes induced by different long-pulsed lasers. The simulation results show that the computational method can capture the key phenomena in the laser-induced cavitation problems, including non-spherical bubble expansion, shock waves, and the ``Moses effect''. Additionally, the observed complex non-spherical shapes of vapor bubbles generated by long-pulsed laser reflect some characteristics (e.g., direction, width) of the laser beam. The dissertation also investigates the relation between bubble shapes and laser parameters and explores the transition between two commonly observed shapes -- namely, a rounded pear-like shape and an elongated conical shape -- using the proposed computational model. Two laboratory experiments are simulated, in which Holmium:YAG and Thulium fiber lasers are used respectively to generate bubbles of different shapes. In both cases, the predicted bubble nucleation and morphology agree reasonably well with the experimental observation. The full-field results of laser radiance, temperature, velocity, and pressure are analyzed to explain bubble dynamics and energy transmission. It is found that due to the lasting energy input, the vapor bubble's dynamics is driven not only by advection, but also by the continued vaporization at its surface. Vaporization lasts less than 1 microsecond in the case of the pear-shaped bubble, compared to over 50 microseconds for the elongated bubble. It is thus hypothesized that the bubble's morphology is determined by a competition between the speed of bubble growth due to advection and continuous vaporization. When the speed of advection is higher than that of vaporization, the bubble tends to grow spherically. Otherwise, it elongates along the laser beam direction. To test this hypothesis, the two speeds are defined analytically using a model problem and then estimated for the experiments using simulation results. The results support the hypothesis and also suggest that when the laser's power is fixed, a higher laser absorption coefficient and a narrower beam facilitate bubble elongation. / Doctor of Philosophy / Laser-induced cavitation is a process where laser beams create bubbles in a liquid. This phenomenon is widely applied in research and microfluidic applications for precise control of bubble dynamics. It also naturally occurs in various laser-based processes involving liquid environments. Understanding laser-induced cavitation is important for enhancing the effectiveness and safety of related technologies. However, experimental studies encounter limitations, highlighting the development of numerical methods to advance the understanding of laser-induced cavitation. The laser-induced cavitation can be roughly described as localized boiling through thermal radiation. The detailed physics involves the absorption of laser light by a liquid, the formation of vapor bubbles due to localized heating, and the dynamics of both the bubbles and the surrounding liquid. The first part of the dissertation introduces a new computational method for modeling these phenomena. The dynamics of the two-phase flow are modeled by the Navier-Stokes equations, which are solved using the FInite Volume method with Exact two-phase Riemann solvers (FIVER). The absorption of the laser light is modeled by a new laser radiation equation, which is derived from laser energy conservation and special properties of the laser. An embedded boundary finite volume method is developed to solve this equation on the same mesh created for the NS equations. Additionally, a method of latent heat reservoir is developed to predict the onset of vaporization. In this work, the level set method is employed to track the bubble surface, and a method of local correction and reinitialization is developed to account for possible continuous phase transitions. After developing this new method, several test cases are simulated. The simulation results show that the method can capture the key phenomena in the laser-induced cavitation problems, including the absorption of laser light, non-spherical bubble expansion, and shock waves. When the laser pulse is comparable to or longer than the acoustic time scale (long-pulsed laser), vapor bubbles generated often have complex non-spherical shapes. The bubble shapes reflect some characteristics (e.g., direction, width) of the laser beam. The second part of the dissertation investigates the relation between bubble shapes and laser parameters. Two laboratory experiments are simulated, in which two different lasers are used to generate bubbles of different shapes, namely, a rounded pear-like shape and an elongated conical shape. In both cases, the simulated bubbles exhibit shapes and sizes that reasonably match the experimental results. The simulation results of temperature, pressure, and velocity fields are analyzed to explain bubble dynamics and energy transmission. The analysis shows that the expansion of bubbles induced by long-pulsed lasers is determined not only by advection but also by the continued vaporization at its surface. Vaporization lasts less than $1$ microsecond in the case of the pear-shaped bubble, compared to over $50$ microseconds for the elongated bubble. It is thus hypothesized that the bubble expansion is determined by a competition between the speed of bubble growth due to advection and continuous vaporization. When the speed of advection is higher than that of vaporization, the bubble tends to grow spherically. Otherwise, it elongates along the laser beam direction. To test this hypothesis, the two speeds are defined analytically using a model problem and then estimated for the experiments using simulation results. The results support the hypothesis and also suggest that when the laser's power is fixed, a higher laser absorption coefficient and a narrower beam facilitate bubble elongation.