The unbalance moments at the edge connections of flat plate structures induced by lateral forces (i.e. an earthquake) may not always act in parallel directions of the building axes. Most research studied the unbalanced moments in one direction, a few of them in biaxial directions, and none of them in incline directions. This paper presents the results of a nonlinear finite element analysis on punching shear capacity at edge column-slab connections subjected to three directions of the unbalanced moments namely perpendicular, incline 45°, and parallel to the slab free edge in combination with the shear force. A 3-D numerical analysis of ten isolated edge column-plate connections was conducted by applying an appropriate element size, mesh, and calibrated material parameters of the concrete damage plasticity (CDP) model in ABAQUS. the connections were subjected to ten variations of the moment to shear (M/V) ratios. The results show that the punching shear capacity decreases exponentially for the unbalanced moment acting perpendicular and parallel to the slab free edge, and linearly for unbalanced moment incline 45° as the increase in M/V ratio. The M-V interaction at the edge connections depends on the unbalanced moment directions which are slightly different from the ACI 318 code.