An effective design sensitivity calculation technique based on the implicit differentiation method is formulated for isoparametric boundary elements for two-dimensional shape optimization problems, and a practical algorithm for the displacement and stress sensitivities on the boundary is proposed. Efficiency and accuracy of the technique is compared with the semi-analytic method by implementing the sensitivity analysis of typical basic shape design problems. The technique is also applied to the minimum weight design under stress constraints, and an optimal shape of an elliptic hole in a square plate is determined under biaxial uniform tension loading.