In this paper, the natural frequencies of the radial vibrations of a hollow cylinder and hollow sphere with different boundary conditions under influences of rotation and non-homogeneity have been studied. The radial vibrations of orthotropic material as affected by the angular velocity are investigated on the basis of the linear theory of elasticity. The of elastodynamic equations have been solved in analytical form. Numerical results are given and illustrated graphically for each case. Comparisons are made with previous results which given in the absence of rotation and non-homogeneity. The results indicate that the effect of rotation and non-homogeneity is very pronounced.