The possibility of propagation of Rayleigh waves in an incompressible crust of constant density and rigidity varying exponentially with depth lying on (i) a semi-infinite incompressible homogeneous medium and (ii) a semi-infinite compressible homogeneous medium is studied in this paper. The variation of rigidity is assumed as , where b and β are constants. To fix ideas we suppose that the crust has the thickness 37.5 km. in which the rigidity increases exponentially from 2.747 × 1011 to 4.53 × 1011 dynes/cm2 over the ultrabasic material of infinite depth in which the rigidity is constant and equal to 6.47 × 1011 dynes/cm2. Frequency equations and their numerical solutions are obtained in both the cases. The results thus obtained are compared with the results derived from those given by Newlands.