The present work describes a formulation for computing design sensitivities required in inverse problems and shape optimization of solid objects, in the frame of the hybrid boundary element method. The so-called direct differentiation method is applied in order to calculate the gradients, i.e. the implicit diferentiation of the discretized boundary is performed, resulting in a general and efficient analysis technique for shape design sensitivity analysis of all structural quantities. It is demonstrated that the resulting sensitivities matrices present some useful spectral properties, which are related to the matrix spectral properties of the basic hybrid formulation. This formulation is valid for tridimensional solids, although only potential and bidimensional applications are considered as particular cases. The singularities that appear in the resulting boundary integrals are exactly the same which have already been dealt with in the basic formulation. The analytical and numerical procedures were performed by using the mathematical package Maple V release 3. Linear boundary elements were used for both potential and elasticity problems. Numerical results obtained by the present procedure are compared to finite differences results to demonstrate the effectiveness of the present formulation.