An alternative design method for interior flat plate-column connections subjected to punching shear and unbalanced moment was developed. Since the slab-column connections are severely damaged by flexural cracking before punching shear failure, punching shear was assumed to be resisted mainly by the compression zone of the slab critical section. Considering the interaction with the flexural moment of the slab, the punching shear strength of the compression zone was evaluated based on the material failure criteria of concrete subjected to multiple stresses. The punching shear strength was also used to evaluate the unbalanced moment capacity of the slab-column connections. For verification, the proposed strength model was applied to existing test specimens subjected to direct punching shear or combined punching shear and unbalanced moment. The results showed that the proposed method predicted the strengths of the test specimens better than current design methods in ACI 318 and Eurocode 2.