Abstract: After the development for decades, the BEM has been regarded as an important supplement of the FEM in academic community. However, to make it become the actual need in engineering, it must solve some problems which are difficult to be solved by the FEM and other methods. In order to give full play to its advantage of higher accuracy, and to obtain reliable results for some complex problems, the author presented a high accuracy BEM scheme in recent years through error analysis, and it can also obtain the converged solution of the BEM in the absence of analytical and other numerical solutions for comparison. An important application of this new scheme is the local stress analysis of a real beam, a plate and a shell structure, and that is the high accuracy 3D BE analysis of the beam, plate and shell combined with the peripheral structural members or foundations, considering the real geometrical details. Two examples of 2D high accuracy BE analysis are presented, one for transverse bending of a real clamped thin-plate beam, and another for a stiffened circular cylindrical shell. The former reveals that the local stress on the cantilever end is much higher than the stress obtained by the beam bending theory. A 3D BE model for a real clamped thin-plate beam is constructed, and the boundary degrees of freedom beyond the limit of scale can be solved on PC using conventional BEM. Thusly, it must be solved by the high performance BEM, namely the high accuracy BE analysis combined with fast algorithms. Finally, the author look forward some future work on these two related new fields, hoping to play a valuable role.