In this paper, a numerical modeling of contact conical transducers is discussed in conjunction with wave propagation analyses by a finite difference method (FDM). Although transducers are the devices to convert electrical energy into mechanical energy and vice versa, attention in this paper is paid mostly to the study of characteristics and parameters of cones and wedges influencing their performance. Cones and wedges inserted between an ultrasonic transducer and the specimen provide the transducer with enhanced capability for point or line contact with the specimen. We study the effect of the dimensions, shape and aperture on the frequency response and the angle of incidence of the wave. Through the testing transducer modeling, some conclusions have been drawn from the analysis, which is useful to as the guideline and criteria for an optimum conical wedge design.