In this paper we study vector-valued almost minimizers of the energy functional integral(D)(vertical bar del u vertical bar(2) + 2 vertical bar u vertical bar) dx. We establish the regularity for both minimizers and the "regular" part of the free boundary. The analysis of the free boundary is based on Weiss-type monotonicity formula and the epiperimetric inequality for the energy minimizers. (C) 2022 The Author(s). Published by Elsevier Inc.