Cylindrical shells are used for a variety of engineering applications such as undersea vehicles and aircraft. The models currently used to determine the vibration characteristics of these shells are often approximated by assuming the shell is infinitely long or has shear-diaphragm boundary conditions. These models also ignore complex loading conditions such as plane waves in favor of point forces or free vibration models. This work expands on the capabilities of these models by examining the acoustic response of a finite length cylinder with flat plate endcaps to multiple types of distributed loading conditions. Starting with the Donnell equations of motion for thin cylinders and the classical plate theory equations of motion for the endcaps, spacial domain displacement field solutions for the shell and plates take an assumed form that includes unknown wave propagation coefficients. These solutions are substituted into stress boundary conditions and continuity equations evaluated at the intersections between the shell and plates. An infinite summation is contained within the boundary conditions and continuity equations which is decoupled, truncated, and compiled in matrix form to allow for the propagation coefficients to be found via a convergent sum of vectors. System responses due to a ring loading and multiple cases of plane waves are studied and validated using a finite element analysis of the system. It is shown that the analytical model matches the finite element model well. / Master of Science / Cylindrical shells are used for a variety of engineering applications such as undersea vehicles and aircraft. The mathematical models currently used to determine the motion of the shell use approximate methods that can be inaccurate. Often, these models do not apply to forces such as those involved in sonar signals. This work analyses a new model that examines the vibration of a finite length cylinder with flat plate endcaps to multiple types of forces. Standard theories are used to calculate the vibration of the shell and endcaps where the motion of the shell and plates is assumed to follow a specific pattern. Linear algebra techniques are then used to produce the formulas for the motion of the shell. The vibration of the system is validated using a finite element analysis. It is shown that the mathematical model matches the finite element model well.