In many areas of acoustical imaging, such as ultrasonic non-destructive evaluation (NDE), a realistic calculation of ultrasonic field parameters and associated elastic wave scattering requires the treatment of discontinuous, layered solids in complex geometries. These facts suggest the need for an accurate and geometrically flexible numerical approach for the simulation of the ultrasonic field, rather than reliance on semi-analytic solutions.In this paper we present an approach for solving the elastic wave equation in discontinuous scattering related to ultrasonic NDE are presented as evidence of the accuracy and flexibility of the proposed computational method.