New optimality conditions are derived for a class of shape optimization problems. The conditions are established on the boundary by an application of the boundary variations technique and in the interior of an optimal domain by exploiting the topological derivative method. An example is provided for which the classical second order sufficient optimality conditions are verified for an optimal simply connected domain. However, the value of the cost can be improved by the topology variations, and therefore, the optimal solution can be substantially changed by applying the topology optimization.