Based on separation of variables and within three-dimensional theory of elasticity, we derive a solution of the problem of forced harmonic oscillations of shallow shells in accounting for different variants of energy dissipation. We derive an exact solution for plates within the accuracy of computing and an exact solution for shallow shells within the known assumptions of the theory of shallow shells. We also develop a simplified model for shallow shells subjected to dynamic impact in accounting for energy dissipation. The model generalizes discrete-structural and continuous-structural approaches used when developing simplified models for analysis of laminated structures.