Reinforced cylindrical shells are used in numerous industries; common examples include undersea vehicles and industrial piping. Current models typically incorporate approximate theories to determine shell behavior, which have limitations in terms of both thickness and frequency. In addition, many applications feature coatings on the shell surface that normally have thicknesses which must also be considered. To increase the fidelity of such systems, this work develops an analytical model of an elastic cylindrical shell featuring periodically spaced ring stiffeners with an acoustic coating applied to the outer surface. There is an external fluid environment. Beginning with the equations of elasticity for a solid, spatial-domain displacement field solutions are produced incorporating unknown wave propagation coefficients. These fields are used to determine stresses at the boundaries of the shell and coating, which are then coupled with stresses from the stiffeners and fluid. The stress boundary conditions contain double-index infinite summations, which are decoupled, truncated, and recombined into a global matrix equation. The solution to this global equation results in the displacement responses of the system as well as the scattered pressure field. Two distinct loadings are considered: a ring loading and an incident acoustic wave. Thin-shell reference models are used for validation, and the acoustic response of the system is examined. It is shown that the reinforcing ribs and acoustic coating have a considerable effect on system behavior. / Master of Science