Abstract: The difficulty of the evaluation of nearly singular integrals has hindered the applications of the boundary element method in engineering. A semi-analytic algorithm established by the first author can efficiently compute the nearly singular integrals. Based on the algorithm, exact formulations are obtained for calculating the nearly hyper-singular integrals on the linear element and a flat element. As a result, numerical quadrature is avoided. Furthermore, the strategy is applicable to some high-order elements. Consequently, the boundary element method is enabled to deal with thin-walled structures in elasticity problems. Numerical results illustrate the accuracy and effectiveness of the algorithm.