The failure mode of the wide-shallow bucket foundation is different from that of the traditional suction caisson and the narrow-deep bucket foundation. Results from elasto-plastic analyses of 3D finite element models are presented, aimed at defining the shape of the yield envelope in the V–H, V–M, H–M and V–H–M spaces and the failure mode of the bucket foundation. The compressive bearing capacity of the wide-shallow bucket foundation was determined by the displacement. The corresponding load under a vertical displacement of 0.06D was the vertical ultimate bearing capacity. The vertical loading had an amplification effect on the horizontal load-bearing and moment capacity, and the horizontal loading which was in the opposite direction to the moment increased the moment capacity by 20–40%. New simplified calculation methods were proposed for the vertical load-bearing capacity and the overturning stability. In the proposed method, the vertical capacity consisted of a top plate resistance of the bucket and a side frictional resistance. The overturning stability was determined by the safety factor method, and depended on the location of the rotation point. A comparison between results from the finite element analysis and the simplified calculation methods showed that the proposed equations properly predicted the capacities of the wide-shallow bucket foundations.