At present there are many theories for describing elastic bodies in general relativity. Aside from the problem of choosing the theory, there exists the problem of choosing the metric of a pre-stressed state. Frequently, the pre-stressed state of an elastic sphere is assigned the metric of flat space. This is the reason for paradoxical solutions in the case of a homogeneous sphere with constant density. In the present article it is supposed that the metric of the pre-stressed state describes a curved space, and can be expressed by the use of the displacement vector function. To test this supposition, we solve the problem of an elastic homogeneous sphere in the classical and relativistic case. The relativistic solution approximates the classical solution in the case of the small fields.
