[en] In the paper the elastic Schwarzschild interior solution for spherically symmetric elastic matter is studied. It is shown that in the case of certain type of homogeneity (''material hcmogeneity'') the problem can be reduced to an ordinary non-linear differential equation, whose certain solutions describe finite spheres. The calculations are performed in the Rayner's formalism modified by Carter and Quintana. As an example the homogeneous model of the Earth is discussed. (Sz.N.Z.)