In this work, we compute the shape derivatives of eigenvalues problem for elliptic operators associated to various boundary conditions, that is Dirichlet, Neumann, Robin, and Wentzell boundary conditions. We also consider the case when the conductivity and the density have jumps, which corresponds to composite structures. The proposed method is based on a result for the derivative of a minimum with respect to a parameter. The main advantage is that the procedure exposed in this work is uniform and efficient with respect to the computations. Indeed, in order to underline this efficiency, we present in the appendix the computation in the case of the mixture of two phases using the classical method based on the material derivative, which turns out to be much more tedious.