In this work, using new inverse trigonometric kinematic displacement function, the bending solution of simply supported isotropic and transversely isotopic thin, moderately thin and thick square plates with aspect ratio variations is given. The paper introduces a new inverse trigonometric shear deformation theory (nITSDT) for the bi-directional bending study, which is variationally compatible. The transverse shear stress can be obtained directly from the constitutive relationships on the top and bottom surfaces of the plate that satisfy the shear stress free surface conditions, so the theory does not need a factor for shear correction. The dynamic version of the virtual work principle is used to obtain the governing equations and boundary conditions of the theory. The Finite Element (FE) solution has been developed using MATLAB code based on the present theory for simply supported laminated composite plates. In order to illustrate the efficiency of the proposed theory, the results of displacements and stresses are compared with those of other refined theories and exact solution. The findings obtained from the use of the theory are found to agree well with the precise results of elasticity.