In this paper, the deformation and the corresponding stresses in a non-homogeneous elastic rotating about its axis with a constant angular velocity is investigated. The problem involving a half-space or an infinite space with a cylindrical or spherical cavity have been subjected to certain boundary conditions. The material is thermo-elastic and has an non-homogeneous in the direction perpendicular to the boundary surface for the half-space problem with a cylindrical or spherical cavity. The system of fundamental equations is solved by means of a finite-difference method and the numerical calculations are carried out for the temperature, displacement and the components of stresses. Numerical results have been given and illustrated graphically for each case considered. The results indicate that the effect of rotation and non-homogeneity are very pronounced. Comparison made with the results predicted by the theory of thermo elasticity in the absence of rotation.