The undrained pure translational and torsional capacity of anchors and the plate response under eccentric translational loading is investigated in this paper using three-dimensional finite element (3D-FE) analysis. Plastic limit analysis is adopted to establish a benchmark solution for ultimate translational resistance with satisfactory agreement with the FE values which confirms the developed numerical model. Although plate thickness has a marked impact on the maximum shear and torsion resistance, the shape of failure envelope is minimally affected by thickness. A simple three-degree-of-freedom interaction equation is curve-fitted to FE failure datapoints. Representative interaction relationships are introduced for square and rectangular plates.