Abstract: The finite element method was used to deal with the steady linear elasticity equations, and the C-Bézier basis function was used as the shape function on the reference element of the elasticity equations. By selecting the appropriate shape parameters, the accuracy of the numerical solution was three orders of magnitude higher than that of the traditional Lagrange basis in L^∞、L² norm and 2~6 orders of magnitude higher in H¹semi-norm. It sufficiently showed that C-Bézier basis has better approximation effect in simulating steady linear elasticity equations.