An inverse approach based on the inherent strain method [ASME J. Engng Mater. Technol. 111 (1989) 1; Determination of residual stress based on the estimation of eigenstrain, PhD Thesis, 1996] using BEM has been proposed for constructing the residual stress existing in structures. Considering the stability of the inverse problem, the inherent strain field is approximately expressed as a series of some smooth basis functions, and the corresponding domain integral is transformed into boundary integral by means of the dual reciprocity boundary element method. In this way the advantage of the BE approach can be preserved. Numerical examples show the applicability of the presented scheme.