Plastic failure of thick axisymmetric plates obeying Mises yield criterion is theoretically investigated. Upper and lower bounds for yield loci under the combination of bi-directional bending moments and a shear force are formulated explicitly, and they are found very close in size as well as in shape. The theoretical results are applied to annular plates subjected to uniform line loads along the circular edges, and some numerical solutions are demonstrated for four cases of support conditions. Two series of collapse tests of steel nuts are performed to provide load carrying capacities, which are found in favor of the theory.