In this paper, under assumptions that the nominal linear singular system is regular and impulse-free, and has all its finite eigenvalues lying inside certain specified regions, a sufficient condition is proposed to preserve the assumed properties when both structured (elemental) and unstructured (norm-bounded) parameter perturbations are added into the nominal singular system. No restriction is imposed on the shapes of the specified regions. The proposed method is applicable to both the continuous-time case and the discrete-time case. When all the finite eigenvalues are just required to locate in the stable region, the proposed criterion will become the stability robustness criterion. For the case that the linear singular system only subjects to structured perturbations, by an illustrated example, the presented sufficient condition is shown to be less conservative than the existing one reported recently in the literature.