n algorithm using the boundary element method (BEM) is demonstrated for problems in two-dimensional elastostatics. The algorithm is based on the weakly singular Somigliana stress identity in which the linear state regularizing field is extended over the entire surface. The linear state regularizing field is given by the first two terms of a Taylor series expansion of the displacement field at the source point and the tractions associated with the constant stress solution. The BEM algorithm satisfies the...