This paper describes a new algorithm, named the Sensitive Pole Algorithm, for the automatic computation of the eigenvalues (poles) most sensitive to parameter changes in large-scale system matrices. The effectiveness and robustness of the algorithm in tracing root-locus plots is illustrated by numerical results from the small-signal stability analysis of realistic power system models. The algorithm can be used in many other fields of engineering that also study the impact of parametric changes to linear system models.Index Terms-Eigenvalues, eigenvalue sensitivity, large-scale eigenvalue problems, parametric stability margins, poles, power system dynamic stability, power system stability, root loci, small-signal stability, system oscillations, transfer functions.