Abstract The nonlinear mechanics of sandwich plates is studied using a layerwise third-order thickness and shear deformation theory. In particular, the two face sheets are modelled using a second-order shear deformation theory (well-justified in case of a zero-shear stress only at one outer surface) and the core is modelled with a third-order thickness and transverse shear deformation theory. After introducing continuity of displacements at the interfaces between the core and the face sheets, 16 independent kinematic parameters are retained. An independent parameter is kept to describe the thickness deformation, which allows for introduction of the corresponding boundary condition; this represents a significant novel contribution. Geometric nonlinearity in all the kinematic parameters is introduced. Numerical results are presented for deflection of a sandwich plate under pressure. A thin core was considered, since it is numerically more critical, and a wide range of core stiffnesses was studied in order to verify the validity of the proposed model till the limit case of two plates joined by a core of negligible stiffness (i.e., two independent plates). Numerical results are compared to those obtained by a commercial finite element (FE) program with three-dimensional solid elements till the limit when the FE code fails for large deformations of the extremely weak core.