Analytical models have been used here to conduct detailed studies on the elastoplastic response of rectangular plates subjected to normal impact of a rigid sphere. Analytical models have been derived using a complete modelling approach in which the equations of motion of the contacting bodies (i.e. the plate and spherical impactor) and a compliance law for the local contact mechanics are used to formulate the impact model. To account for the local contact mechanics, a novel Meyer-type compliance model based on elastic-elastoplastic-fully plastic material behaviour has been formulated and validated using published experimental results. This compliance model was used to investigate the elastoplastic impact response of both transversely inflexible and transversely flexible rectangular plates. Particular attention has been given to solving the nonlinear impact models, leading to the development of a new algorithm to solve the nonlinear models of a half-space impact. The algorithm is simple, inherently stable and converges very quickly. For transversely flexible plate impact, investigations were centred on the elastoplastic impact response of a three-layer laminated plate structure called a trimorph plate. The understanding gained from investigating the elastoplastic impact response of an Al/PVDF/PZT trimorph plate was applied to study a newly proposed strategy for active mitigation of elastoplastic impact effects i.e. plastic deformation and/or damage. The idea behind the strategy was to use bonded piezoactuators to actively induce a state of pre-stress in the host layer, which in turn influenced the impact response of the plate. A preliminary qualitative analysis of the proposed strategy was conducted using analytically derived models for a PZT/Al/PZT trimorph plate and the results obtained showed that the proposed strategy can be used to achieve significant levels of mitigation against elastoplastic impact effects.