In this paper, a new derivative-free method for Worst Case Analysis (WCA) of circuit design is defined. A WCA of a device can be performed by solving a particular minimization problem where the objective function values are obtained by a simulation code and where some variables are subject to a spherical constraint and others to box constraints. In order to efficiently tackle such a problem, the paper defines a new DF algorithm which follows a two blocks Gauss Seidel approach, namely it alternates an approximated minimization with respect to the variables subject to the spherical constraint with an approximated minimization respect to the variables subject to the box constraints. The algorithm is described and its global convergence properties are analyzed. Furthermore it is tested in the WCA of a MOSFET operational amplifier and its computational behaviour is compared with the one of the efficient optimization tool of the WiCkeD suite for circuit analysis. The obtained results seem to indicate that the proposed algorithm is promising in terms of average efficiency, accuracy and robustness.