In this work, the field concentration and distribution along the wall of elliptic holes in three-dimensional thick plates of anisotropic magneto-electro-elastic (MEE) materials are systematically analyzed using a three-dimensional weak finite-element formulation implemented in the COMSOL software. The proposed model is validated against existing solutions, and then applied to the analysis and design of multiferroic composites with an open hole, including multicoated circular fibrous MEE composites and MEE sandwich made of piezoelectric (BaTiO3) and magnetostrictive (CoFe2O4) materials. The distribution of field concentration factor, hoop stress, radial stress, and out-of-plane stress along the wall of elliptic holes for MEE plates under typical far-ﬁeld uniform loads are analyzed, as well as the influence of hole shape, plate thickness and stacking sequence. Under far-field electric or magnetic fields, various unique features are observed which should be very helpful for strength and fatigue designs of MEE materials with notches and holes. An empirical formula is derived to predict accurately the maximum stress concentration factor along the thickness direction of the elliptical hole.