Abstract: An inverse approach based on the inherent strain method using BEM is proposed for constructing the planar residual stresses existing in structures that are in self-equilibrium. Considering the stability of the inverse approach, the inherent strain field is approximately expressed as a series of smooth basis functions, such as polynomials and trigonometric functions. In order to identify the residual stress induced by shear inherent strain, the specific solution expressions of displacement and traction corresponding to inherent strain are given, and the domain integral is transformed into boundary integral using the dual reciprocity boundary element method so that the advantage of the BE approach is preserved. The explicit expression of the sensitivity matrix is derived to enhance the efficiency of the inverse approach. Two numerical examples are given to show the applicability of the presented scheme.