  This paper is concerned with a Galerkin boundary element method solving the
two dimensional exterior elastic wave scattering problem. The original problem
is first reduced to the so-called Burton-Miller (\cite{BM71}) boundary integral
formulation, and essential mathematical features of its variational form are
discussed. In numerical implementations, a newly-derived and analytically
accurate regularization formula (\cite{YHX}) is employed for the numerical
evaluation of hyper-singular boundary integral operator. A new computational
approach is employed based on the series expansions of Hankel functions for the
computation of weakly-singular boundary integral operators during the reduction
of corresponding Galerkin equations into a discrete linear system. The
effectiveness of proposed numerical methods is demonstrated using several
numerical examples.
