This paper presents the static response of advanced composite plates by using a new non-polynomial higher order shear deformation theory (HSDT). The present theory accounts for non-linear in plane displacement and constant transverse displacement through the plate thickness, complies with plate surface boundary conditions, and in this manner a shear correction factor is not required. Navier closed-form solution is obtained for functionally grade plates (FGPs) subjected to transverse loads for simply supported boundary conditions. The optimization of the shear strain function and bi-sinusoidal load is adopted in this publication. The novelty of this work is the geometry used, stretching effect is not applied and the amount of unknown displacement functions are 5. In addition to the optimization, the inclusion of an exponential function to the tangent function is an interesting feature in this paper. The accuracy of the present HSDT is discussed by comparing the results with an existing quasi-3D exact solution and several HSDTs results. It is concluded that the present non-polynomial HSDT, is more effective than the well-known trigonometric HSDT for well-known example problems available in the literature. © 2013 Elsevier Ltd. All rights reserved.