Inverse analysis using the boundary element method is considered theoretically very useful for the qantitative estimation of complicated stresses in a solid material induced by machining, heating and so on. However, a more refined fundamental consideration is still needed for a reliable evaluation of the stresses. In order to fined a more practical estimation method, the authors have carried out several numerical simulations by using rectangular plate models with residual stresses induced by spot heating in the plate. They have also made an improved identification program of the boundary element method. Through typical calculations using this program, they found that unknown residual stress distribution in the plate was identified with enough accuracy from input data of the boundary displacements and tractions.