Local influence is a method of sensitivity analysis for assessing the influence of small perturbations in a general statistical model. In the present paper, this popular method is applied to multivariate elliptical linear regression models. Several schemes of perturbation, including perturbations in case-weights, explanatory variables and response variables are considered. The observed information matrix under the postulated model and Delta matrices under the corresponding perturbed models are derived. Assessment of local influence is made.