Analysis of the flow field in a laser engine represents a difficult computational problem involving combinations of complex physical and gas-dynamical processes. Following a brief discussion of these processes a calculation procedure using primitive variables formulation on a non-staggered grid system is introduced. Based on this procedure, a Pressure Based Navier-Stokes Solver (PBNS) is developed using a generalized curvilinear coordinate system. The solver is first tested in application to a subsonic compressible flow over an insulated flat plate and to a flow in an axisymmetric converging-diverging nozzle. Next, the PBNS code is used to analyze the flowfield and performance of a laser thruster. The physical/numerical model includes the geometric ray tracing for the laser beam, beam power absorption, plasma radiation losses, and plasma thermophysical and optical properties. Equilibrium hydrogen is used as a flowing gas and its properties are calculated using the Hydrogen Properties Calculation (HPC) based on the the methods of statistical thermodynamics. Two thruster configurations, two laser types (CO₂ and iodide), various laser power levels, and various injection conditions are tested. The results of these tests include the temperature, pressure, velocity and Mach number contours, as well as table of the laser beam power absorbed, radiation losses to the thruster walls, thrust level and specific impulse. The maximum specific impulse obtained in these tests is 1537 sec for a CO₂ laser thruster and 827 sec for an iodide laser thruster. Up to 100% power absorption can be achieved, however, the radiation losses from the hot plasma are quite high disallowing a full conversion of the absorbed power into the thermal energy of the propellant. The PBNS code can be used to study the effects of various design parameters on the performance of a laser thruster and provide guidelines for the preliminary design of a laser engine. / Ph. D.