This paper presents a generalized higher order shear deformation theory (HSDT) and its finite element formulation for the bending analysis of advanced composite plates such as functionally graded plates (FGPs). New shear strain shape functions are presented. The generalized HSDT accounts for non-linear and constant variation of in-plane and transverse displacement respectively through the plate thickness, complies with plate surface boundary conditions and do not require shear correction factors. The generalized finite element code is base on a continuous isoparametric Lagrangian finite element with seven degrees of freedom per node. Numerical results for different side-to-thickness ratio, aspect ratios, volume fraction, and simply supported boundary conditions are compared. Results show that new non-polynomial HSDTs solved by the proposed generalized finite element technique are more accurate than, for example, the well-known trigonometric HSDT, having the same DOFs. It is concluded that some non-polynomial shear strain shape functions are more effective than the polynomials counterparts. © 2012 Elsevier Ltd.