This paper utilizes weak-form variational principle to determine the nonlinear natural frequencies of highly clamped rectangular isotropic plates. The energy functional was formulated using weak-form variational statement on the integral function of the plate problem. The displacement functions were developed based on static deflections of orthogonal beam network. The algebraic expression for stress function was determined using direct integration process on compatibility equation. The amplitude of deflection which influences the geometric nonlinearity of the plate was determined using integration process on energy functional based on static equilibrium equations. The stiffness and mass matrices were developed from the expressions of energy functional based on dynamic equilibrium equations. The nonlinear natural frequencies were numerically computed. The validation of the results using the results from previous work found in literature shows satisfactory convergence, with an error of 0.034%. Conclusively, weak-form variational principle gives satisfactory approximation to nonlinear vibration analysis of rectangular isotropic plates.