Abstract The paper investigates the influence of biaxial loading on punching resistance at square and elongated edge columns of flat slabs which is virtually neglected in the literature. In the absence of experimental data, the influence of biaxial loading is determined using nonlinear finite element analysis (NLFEA) with 3D solid elements. The resulting baseline punching resistances are compared with the predictions of various implementations of the Critical Shear Crack Theory (CSCT) including a Joint Shell Punching Model (JSPME) in which punching failure is simulated using nonlinear joint elements inserted between the nodes of nonlinear shell elements located around the punching control perimeter. The failure criterion of the JSPME, which is most suited for structural assessment, implicitly accounts for the effect of biaxial loading unlike the original (classic) and closed form versions of the CSCT. The classic CSCT indirectly accounts for loading eccentricity by reducing the punching control perimeter by a multiple ke which is determined in this paper using shear field analysis. Conversely, the closed form CSCT, which is adopted in the draft for the next generation of Eurocode 2 (EC2), enhances the design shear force by a multiple β. The paper uses experimental data to determine an expression for β for edge column connections subject to inwards eccentricity normal to the slab edge. Subsequently, shear field analysis on representative flat slab to edge column connections is used to extend this expression for β to edge column connections subject to biaxial eccentricity. NLFEA simulations with 3D solid elements are used to validate the predictions of the JSPME, the shear field methodology used to determine ke in the classic CSCT and the proposed expression for β in the closed form CSCT. Reasonable agreement is achieved between all these analysis methods. The main advantage of the JSPME over NLFEA with 3D solid elements is its increased computational efficiency which makes it more suitable for the assessment of large structures.