The nonstationary behavior of reinforced compound structures is analyzed within the framework of the geometrically nonlinear Timoshenko theory of shells and rods. The numerical method used to solve the problem is based on the finite-difference approximation of the original differential equations. The dynamic behavior of a reinforced compound structure under nonstationary loading is demonstrated by way of a numerical example. The numerical results are compared with experimental data Keywords: reinforced discrete shell, Timoshenko shell theory, nonstationary loading, numerical method Introduction. Reinforced compound shells are complex, spatially inhomogeneous, elastic structures that include discrete inclusions and areas where the geometrical and material parameters change. These factors complicate problem formulations. In particular, the partial differential equations describing the stress-strain state of the original structures include discontinuities of the first kind of the strain and stress components. This is why special numerical algorithms have been developed to adequately simulate wave processes in shells with singularities.The handbook [4] presents algorithms and programs for design of compound shells under stationary and dynamic loads. The dynamic behavior of compound shells under nonstationary loads is analyzed in the monograph [5]. The nonstationary behavior of reinforced shells of revolution with discrete ribs is studied in [2]. The axisymmetric nonlinear vibrations of discretely reinforced conical shells are examined in [9]. Dynamic problems for reinforced ellipsoidal shells are solved in [13]. Initial deflections are accounted for in [11] in solving dynamic problems for discretely reinforced cylindrical shells under nonstationary loads. The nonaxisymmetric forced vibrations of sandwich cylindrical shells with ribbed core are studied in [12].Here we formulate dynamic problems for compound shells and outline a numerical algorithm for solving them. The algorithm is further used to solve model problems.1. Problem Formulation. Governing Equations. Consider a compound inhomogeneous structure consisting of a compound shell and ring ribs rigidly fixed to it along contact lines (the ribs are supposed to be placed along the coordinate line α 2 ) [1]. Forced vibrations of the structure are modeled by a hyperbolic system of nonlinear differential equations of the Timoshenko theory of shells and curvilinear rods [2]. The variation of the displacements of the shell components across the thickness is described in the coordinate frame ( , ) s z by the formulas