A method for robust amplitude beamforming in linear antenna arrays is presented. The admissible tolerances on the array excitations, described as real-valued intervals, are maximised regardless their nominal values, while guaranteeing that the bounds of the radiated power patterns fit a-priori defined mask constraints. A set of representative numerical results, concerned with different mask constraints as well as comparisons with state-of-the-art approaches, is reported and discussed to assess the effectiveness of the proposed approach