Abstract: A two-stage interpolation Galerkin boundary element method called the Quasi-High Order Element Method (QHOEM) is proposed for solving elastoplastic problems. In the initial stage, it uses high order elements to interpolate the coordinates and the variables. For the numerical integration involved, it further uses interpolation to decompose the high order elements into low order elements so that the existing analytical integration formulas can be applied. By doing this, the proposed method yields good adaptab...