In this work, we extend standard likelihood-based procedures to the multivariate linear model using the scale mixtures of multivariate skew-normal-Cauchy distributions. A simple EM algorithm for iteratively computing maximum likelihood estimates is derived. The observed information matrix is computed analytically to account for standard errors. Some results are obtained from real and simulated datasets to illustrate the usefulness of the proposed model. © 2020 Taylor & Francis Group, LLC.