This paper investigates the structural behaviour of RC flat slabs supported on rectangular interior columns and the influence of the loading conditions (one or two-way bending) on their punching shear strength. The punching shear strength of slabs at rectangular columns can be lower than at equivalent square col- umns with a similar length of the control perimeter. This is due to a potential concentration of shear forces alongthecontrol perimeter. Some, but notall designformulas for punchingdesign, consider thisreduction on strength using empirical factors, which are written in terms of the column geometry only. However, in reality, the concentration of shear forces depends also on the deflected shape of the slab. It is shown in this paper that this can be consistently considered by means of the shear-resisting control perimeter. A sound approach is presented to estimate the shear-resisting control perimeter based on the shear fields of the slab accounting for the loading and boundary conditions. An alternative approach is presented based on the contact pressure in the support region which gives comparable predictions of the shear-resisting con- trol perimeter. Both approaches give a physical explanation of the phenomenon. It is also shown that the model previously developed by the authors for non-axis-symmetrical punching of square columns based onthe critical shear crack theory can also be applied to rectangular columns. Four punching shear tests are presented of slabs with one-way & two-way bending to validate the theoretical models presented. Accurate strength and deformation capacity predictions were obtained for the tests investigated.