Based on a multiv ariate linear regression mo del, we prop ose sev eral generalizations to the multiv ariate classical and mo di ed Cook's distances in order to detect one or more of in uen tial observ ations including the case of linear transformations of the estimated regression parameter. For those distances, we deriv ed the exact distributions and point out a metho d to extend the calculation of exact distributions for sev eral other metrics available in the literature, for the univ ariate and multiv ariate cases. The results are extended to elliptical families not under the assumption of normalit y. An application is describ ed in order to exemplify the metho dology.