SUMMARYThe present paper develops the idea of the boundary strip method, and presents its fundamentals, merits, applications and also some closed-form or non-element solutions based on it. The present approach combines the Boundary Integral Equation Method (BIEM) and the finite strip method, taking the advantages of both. The finite strip method is installed into the BIEM by expanding the unknown parameters of problems in terms of trigonometric series. This combination creates a new powerful numerical method with three advantages over other numerical methods, namely, a shorter computation time, a better accuracy and a reduction of one and a half dimensions in mesh generation. Applications in two-dimensional potential and field problems demonstrate the efficiency and the accuracy of the proposed method. Finally, closed-form presentations for Laplace equation and elastostatics are given, along circular segments.