A design sensitivity calculation technique based on the implicit differentiation method is fomulated for isoparametric boundary elements for three-dimensional(3D) shape optimization problems. The practical sensitivity equations for boundary displacements and stresses are derived, and efficiency and accuracy of the technique are compared with the semi-analytic method by implementing the sensitivity analysis of typical and basic shape design problems numerically. The sensitivity calculation technique is then applied to the minimum weight design problems of 3D bodies under stress constraints, such as the shape optimization of the ellipsoidal cavity in a cube and the connecting rod, where the Taylor series approximation, based on the boundary element sensitivity analysis at current design point, is adopted for the efficient implementation of the optimization.