The flexure of a clamped uniformly-loaded thin isotropic rectangular plate is herein analysed. The deflected surface was approximated using a grid work of beams. Coordinate polynomial deflection function satisfying the geometric boundary conditions was derived. Furthermore, different approximations of the derived polynomial function were developed for the clamped rectangular plate corresponding to the first, second and third approximations. The unknown deflection coefficients of the different deflection functions were obtained using Galerkin method, for different aspect ratios ranging from 1.0 to 2.0 for the different approximations. The numerical values of the computed coefficients were compared with the results from previous works and the degree and pattern of convergence observed. The convergence to the results of the classical solution increased as the number of approximations increased from first to third approximation such that the average percentage difference came to 1.98 %, for maximum deflection and 1.96 % for the maximum span moment of the principal axis in the third approximation. This clearly shows that the present study closely compares with the results of classical solution.