A spheroidal coordinate based T matrix formalism is developed for the description of elastic wave scattering from a collection of obstacles embedded in a homogeneous, unbounded medium. The development of the spheroidal formalism for the scattering from a single obstacle is a refinement of the earlier work of Hackman (1984), a discussion of the extension of this approach to a many inclusion system is a generalization of Lim and Hackman (1992). Calculations are presented for the elastic wave scattering from (single) prolate spheroidal and finite cylindrical objects. The single inclusion calculations presented have bearing on a study of anechoic mechanisms in composite materials presented earlier (Lim and Hackman, 1990). ¿ American Geophysical Union 1994