In this paper a generalized non-polynomial quasi-3D shear deformation theory for advanced composite plates is presented and further discussed. The beauty of this generalized theory relies on its 4-unknowns displacement field, which is even less than the classical first order shear deformation theory (FSDT). Moreover, this generalized theory models the stretching effect due to its quasi-3D nature. The main conclusions after solving the governing equations of functionally graded plates (derived by employing the principle of virtual work and solved via Navier-type closed-form solution) are the following: (a) This theory was not much explored and needs further research, (b) the theory performs very well for non-polynomial shear strain shape functions f(z) and g(z), but not for a hybrid case (non-polynomial and polynomial), (c) an optimization procedure is mandatory to select the parameters directly related to f(z) and g(z), (d) bending results strongly depend on the selected shear strain shape functions and the case dependent problem can be verified.