I would like to start out by listing the principal objectives of our present study, and then discussing our initial efforts along these lines. The main objective is to calculate the angular and the frequency dependence of the ultrasonic energy scattered from a solid ellipsoid of revolution embedded in another solid. This calculation has to take into account mode conversion that takes place at the boundary between the ellipsoid and the medium. A second and integral part of the program is an experimental check on the calculations by way of accurate measurements of both the frequency and angular dependence of the ultrasonic energy scattered in the range of one to fifteen MHz.