Adaptive mesh refinement (AMR) is applied extensively in structural shape optimisation (SSO) applications that utilise the finite element method (FEM) of analysis. The AMR approach requires an automatic mesh generator (AMG), which usually produces unstructured FE meshes. Therefore, an obvious drawback is the necessity to generate new meshes, each of which require a complete FE analysis, for each new shape design. A suitable mesh mapping system that reduces the number of required mesh generations significantly would be of major benefit.With this in mind, a boundary element (BE) based point-tracking method, developed for design sensitivity analysis, is employed very successfully as a robust unstructured mesh mapping system. This paper presents the combined AMR and BE mapping approach applied in SSO. The application of the method is fully described and a number of examples demonstrate the efficiency and robustness of the proposed approach.