The wave propagation in elastic solids covered by a thin layer has received significant attention due to the existence of Sezawa waves in many applications such as medical imaging. With a Helmholtz decomposition in cylindrical coordinates and subsequent solutions with Bessel functions, it is found that the velocity of such Sezawa waves is the same as the one in Cartesian coordinates, but the displacement will be decaying along the radius with eventual conversion to plane waves. The decaying with radius exhibits a strong contrast to the uniform displacement in the Cartesian formulation, and the asymptotic approximation is accurate in the range about one wavelength away from the origin. The displacement components in the vicinity of origin are naturally given in Bessel functions which can be singular, making it more suitable to analyze waves excited by a point source with solutions from cylindrical coordinates. This is particularly important in extracting vital wave properties and reconstructing the waveform in the vicinity of source of excitation with measurement data from the outer region.

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