The transition matrix method for stationary elastic waves is extended to a great class of obstacles characterized by piecewise constant properties. First, the translation properties of the basis functions is used to treat two and, then, several homogeneous obstacles, and thereafter an obstacle with consecutively enclosing layers is considered. It is then indicated how these two basic methods of combination can be applied to treat more complex cases, including an obstacle consisting of several nonenclosing parts. Finally, we give some numerical applications to configurations of spherical and nonspherical obstacles in and below the resonance region.