A fitting curve of stress-strain relation given is applied in numerical analyzing based on Legendre orthogonal polynomial and least square method. The nonlinear constitutive model is employed to examine the shape of an arch dam. For the asymmetries and high water pressure, the safety of High Arch Dam is one of key issues in the design and construction of High Arch Dam. The simulation results show that the basic mechanical performance index is symmetrical distribution. The dam mainly bears pressure and no obvious tensile stress exists in the dam when water level is normal. Material yields in dam heel when 1.4 times overloading is considered. It can be concluded that the dam is reliable and the safety margin is satisfactory.