The effective elastic constant of the GaAs-GaAlAs kind semiconductor superlattice has been obtained by means of the mathod of Green's function in the long Wave approximation. The results show that the effective elastic constant is not greater than that of either kind of the matter which are the components of the superlattice. In the limit of b = 0 and b = a, where a is the period of the superlattice and b is the width of one of the component, the te-sult reduces to the elastic constant of one single medium.