New techniques are presented for the analysis of eigenvalue assignment robustness. The basic idea is to use a root locus approach to ensure that the eigenvalues of a dynamic system under parameter perturbations are restricted in the distinct desired regions. No restriction is imposed on the shapes of the specified regions. Both the norm bound and the element bound for the allowable perturbations are obtained. Scaling techniques are proposed to increase the allowable element bound. The proposed methods are applicable to the continuous-time case as well as to the discrete-time case. When the eigenvalues are just required to locate in the stable region, the proposed criteria will become the stability robustness criteria.