By means of the quadrature rules of computing singular periodic functions, mechanical quadrature methods for solving boundary integral equations of plane elasticty problems are presented, which possess high accuracies and low computing complexities. Moreover, the asymptotic expansions with the odd powers of the errors are shown, so that we not only can improve the accuracy order of the approximations by Richardson extrapolation but also can estimate the errors of the approximations by a posteriori error estimations.
By means of Side-Israeli’s quadrature reules, quadrature methods for solving boundary integral equations of the first kind are presented, which have high accuracy O(h3). Moreover, the asymptotic expansions with the odd pwoers h2μ-1 （μ= 2, 3） of the errors are shown, that is, using extrapolations, we can improve the accuracy order of approximations..
