Plates are common structural elements use in several engineering applications and are subjected to different types of loads, including acoustic excitations. The first satisfactory theory of bending plates is associated with Navier and later Kirchhoff. These theories nevertheless, are deficient as they do not take into account the influence of transverse shear forces on the deformation of plates. Consequently, this work explicitly established a refined plate equation, which considers the effect of shear deformation in line with Vasil’ev approach. The differential equation of plates with shear effect was solved for all edge simply supported (SSSS) condition subjected to uniformly distributed load using orthogonal polynomial method. Numerical solutions in the present study are compared to Navier’s solution based on Kirchhoff’s hypotheses which gives an insignificant percentage difference for membrane plates (-00.308% for h = 0.05m) and thin plates (00.260% for h = 0.15m). However, it is also observed that the percentage difference between the present study and Kirchhoff’s hypotheses is high for fairly thick plates (04.172% for h = 0.40m) due to incorporation of share deformation in the solution. The result presented shows good approximation for analyses of fairy thick and thick Isotropic rectangular plates.