A rigid circular disc embedded in an infinite, isotropic elastic solid is assumed to be excited by a normally-incident plane, harmonic compressional wave. The disc is assumed to be either in perfectly welded or perfectly smooth contact with the surrounding solid. In each case, the problem is reduced to the solution of Fredholm integral equations of the second kind. For the case of the welded contact, exact numeral solutions valid at any given frequency are given. Approximate solutions valid at low and high frequencies are obtained for both cases and are compared with the exact solution. The displacement and compliance of the disc as well as other quantities of interest are presented graphically as functions of frequency.