This paper utilises non-linear finite-element analysis with three-dimensional (3D) solid elements to gain insight into the role of shear reinforcement in increasing punching shear resistance at internal columns of flat slabs. The solid element analysis correctly captures the experimentally observed gradual decrease in concrete contribution to shear resistance with increasing slab rotation and the failure mode but is very computationally demanding. As an alternative, the paper presents a novel approach, in which 3D joint elements are combined with non-linear shell elements. Punching failure is modelled with joint elements positioned around a control perimeter located at 0.5d from the column face (where d is the slab effective depth). The joint elements connect the nodes of shell elements located to either side of the punching control perimeter. The punching resistance of the joints is related to the slab rotation using the failure criterion of the critical shear crack theory. The joint-shell punching model (JSPM) considers punching failure both within the shear-reinforced region and due to crushing of concrete struts near the support region. The JSPM is shown to accurately predict punching resistance while requiring significantly less computation time than 3D solid element modelling.