When an unsymmetric laminated plate is considered, the coupling of in-plane and plate bending problems is unavoidable. The boundary element for the coupled stretching bending analysis was developed previously with suitable complex form fundamental solution. Usually, the singular integrals involved in the boundary element are treated by the conventional methods such as Gaussian quadrature rule for regular functions, logarithmic Gaussian quadrature formulas for the function with logarithmic terms, and the use of finite part integrals for the evaluation in sense of Cauchy principal value, or calculated indirectly through the employment of rigid body movement. To avoid the complexity of the numerical integration with complex form fundamental solution, in this paper we provide the explicit closed-form solutions for the singular integrals, which simplify the computer programming and expedite the numerical computation. And hence, the accuracy and efficiency of the associated boundary elements are improved through the newly derived analytical solutions. (C) 2015 Elsevier Ltd. All rights reserved.