Aimed at the problem that the current elasticity-based mesh deformation method always cannot control some poor elements suffering “negative volume” and extreme distortion, the volume and the extruding constraints on modulus of elasticity were introduced to solve above shortages and a modified elasticity-based method based on these geometry constraints was presented. Combined with Patrick mesh quality measure, the differences between the modified method and the classical method were fully analyzed by testing a 3D cubic model with three types of motion or deformation in wide-range, such as rotation, translation, and stretch. The modified method was applied to simulate the plunging motion of NACA0012 airfoil and stretching deformation of wing. Results show this modified method can improve the robustness of elasticity-based method by constraining poor elements in wide-range of motion or deformation, thus providing a better support for solving the unsteady flow problems.