This paper briefly describes elasticity theory with different moduli and research progress in recent twenty years,analyzes computational results respectively from these two theories to all kinds of engineering structures and concludes that applying different moduli theory to solve some engineering components conforms to the real mechanics performance.This paper also deals with the differences between analytical solution and numerical one.Though finite element method is an effective measure to solve these nonlinear problems,seeking analytical solutions is still a difficulty and goal for some problems.