Abstract: From the symmetry of the coefficient matrix of the constitutive law of linear elastic bodies, one may motivated to consider the corresponding inverse proposition, i.e. whether or not the symmetry of the linear constitutive law implies the perfect elasticity of the body. A positive answer of this question may be made via the construction of an elastic potential function for the body,which indicates that the symmetry of the constitutive equation and the perfect elasticity of body are equivalent.