Abstract: The finite deformation and plasticity will occur when a concrete dam is close to failure. It is very important to study the effect of geometric nonlinearity and material nonlinearity including strain softening on maximum bearing capacity. In this paper, material constitutive relation with strain softening, nonlinear geometry equations and equilibrium differential equations considering geometric nonlinearity are presented. The maximum bearing capacity of a concrete dam is obtained by the over-loading method and Arc-length method used to calculate the peak point and falling branch of the load-displacement curve, then the effect of double nonlinearity, including geometric and material nonlinearity considering strain softening, on the maximum bearing capacity are discussed.