In this paper, static indentation and low velocity impact responses of a fully backed composite sandwich plate subjected to a rigid flat-ended cylindrical indenter/impactor are analytically investigated. The analysis is nonlinear due to nonlinear strain-displacement relation. In contrast to the existed analytical models for the indentation of composite sandwich plates, the stacking sequence of the face sheets can be completely arbitrary in the present model. Furthermore, the effects of the initial in-plane normal and shear forces on the edges of the sandwich plate are also considered. Based on these modifications, an improved contact law (contact force – indentation relation) is derived. The low velocity impact analysis of the problem is performed using a discrete system of spring-mass-dashpot model. The characteristics of the equivalent spring and dashpot are identified from the derived contact law and by incorporating the effect of the dynamic material properties of the sandwich plate. Analytical predictions of the load-indentation response as well as the impact force history are compared well with the experimental results in the literature. The effects of various parameters on both indentation and impact responses of the sandwich plates are qualitatively and quantitatively investigated.