Characterization of near-surface properties of materials by acoustic means is most conveniently done by surface acoustic waves (SAW). A conventional acoustic microscope lens excites focused SAW on the object surface, but with a low efficiency. SAW can be excited with a high efficiency and be focused to a diffraction limited spot using conical wavefronts as obtained from a conical axicon. The purpose of this paper is to present the response of the imaging systems utilizing convergent SAW to certain kind of defects. In particular, circular cylindrical cavities, whose axes are perpendicular to surface, are considered. The scattering of the SAW is formulated with some approximations. SAW incident upon the cavity is initially found as an angular spectrum of plane waves. To apply the boundary conditions, the incident field has to be transformed in a form of superposition of cylindrical waves. Similarly, the scattered field, which is found in the form of outgoing cylindrical SAW'S, is converted back to a plane wave spectrum to complete the formulation. At the end, a formula is obtained for the output voltage in terms of the position and the radius of the cylinder. By considering various locations for the cylinder, the sensitivity of the system around the focal point is studied. Also, by comparing the output voltages for cylinders of different radii, sensitivity of the system to the size of the inhomogeneity is examined. The numerical results are found to be in agreement with the experimental observations.