A simple computational procedure is given to determine the robust stability of matrices containing interval parameter uncertainty. The computation consists of determining the maximal phase difference of the characteristic polynomial, evaluated over the vertices of the uncertain parameter set at each point of the stability boundary, and verifying that this maximal phase difference is less than pi radians. This follows as a direct application of the ’mapping theorem’, which allows us effectively to treat rank-one perturbations of matrices. We discuss the conservatism of the method and show how the solution may be improved to any desired level of accuracy. We give several numerical examples of systems with state-space perturbations, and compare our results with those obtained by other methods.