In this paper a 5-unknowns generalized hybrid-type quasi-3D HSDT for the static analysis of functionally graded single and sandwich plates is presented. Generalized hybrid-type modeling can adopted with any kind of shear strain shape functions for the inplane and transverse displacement, and therefore infinite hybrid-type (non-polynomial, polynomial, mixed type) displacement based shear deformation theory complying with the free surface boundary condition can be obtained. The key feature of this theory is that, in addition to including stretching, it has only 5 unknowns in the displacement field modeling as the first order shear deformation theory (FSDT). The generalized hybrid-type theory is also quasi-3D because the 3D Hooke's law equation is utilized, i.e. σzz≠ 0. The generalized governing equations and boundary conditions are derived by employing the principle of virtual works. A generalized Navier-type closed-form solution is obtained for functionally graded single and sandwich plates subjected to transverse load for simply supported boundary conditions. Analytical results from the new generalized hybrid-type quasi-3D higher order shear deformation theory (HSDT) are compared with the FSDT, other quasi-3D HSDTs, and refined HSDTs. The fundamental conclusions that emerge from the present numerical results suggest that: (a) infinite shears strain shape function can be evaluated by using the present theory; (b) polynomial shear strain functions appear to be a good choice for the implementing of a quasi-3D HSDT based on this generalized quasi-3D hybrid type HSDT; (c) this generalized theory can be as accurate as the 6-unknown generalized hybrid-type quasi-3D HSDT; (d) the best HSDT with stretching effect and 5-unknows can be obtained from the present generalized theory, this can be done by optimizing a theory that for example has a given non-polynomial inplane and transverse shears strain shape functions.