The paper describes equations of circular symmetrical sandwich plates bending for plates with isotropic outer layers and nonlinear elastic filler. Two computer models of circular sandwich plates are proposed: 1) analytical model on the basis of Maple CAS, 2) threedimensional FEM-model. We compare results of analytical model with results of numerical simulation using two problems: 1) the problem of axisymmetric transverse bending of a sandwich plate, 2) the problem of axisymmetric transverse bending of a single-layer plate with linear and nonlinear formulation. The first section of the article describes basic differential equations and analytical model constructing method. FEM-model is described in the second section. Numerical results of computer simulation are showed in the last section of the article.