In this study, a new higher order hyperbolic shear deformation theory for mechanical analysis of cross-ply and angle-ply multilayered plates is developed. Analytical solution to the static and buckling responses of symmetric and anti-symmetric composite laminates is presented. The proposed theory considers secant hyperbolic function of thickness coordinate in the displacement field. Also the developed theory assumes non-linear distribution of displacements and ensures that the top and lower surfaces of the plates have zero shear stresses. The equilibrium equations are obtained by applying the principle of virtual work. The stiffness characteristics of cross-ply and angle-ply laminates are taken into account when solving these governing equations. The closed-form Navier solution satisfying the corresponding boundary conditions is derived for simply supported (SS) composite plates. The results for non-dimensional deflections, and stresses of composite laminates under the effect of sinusoidal and uniform distributed load are thus obtained. The uni-axial and bi-axial loading force are used to evaluate critical buckling loads. Furthermore, the impact of span thickness ratio, aspect ratios, fiber orientation, modulus ratio, etc. on static and buckling analysis plates is also studied. The validity of present formulation is demonstrated by comparing our results with some of the available results in the literature.