Generalized Differential Quadrature Rule(GDQR)was applied to investigate the stability of a complex elastic supported beam on an elastic foundation subjected to a partially tangential force. Based on the motion equations and boundary conditions of an elastic supported beam, the matrix eigenvalue equation consisted of the dynamic equations and boundary conditions was obtained after discreted by GDQR.After analyzing the corresponding eigenvalue equations,the effects of the elastic foundation modulus, shear coefficient, complex boundary conditions on critical load were discussed ,for a clamped-elastic supported beam,the influence of elastic foundation modulus and supported spring stiffness to the instability area was studied and some useful conclusions were obtained. It shows that GDQR is an effective way for solving the stability of such system.