The pounding at the deck and abutment interface of a curved bridge, which occurs during earthquakes after closing the gap, directly leads to the deck unseating, in-plane deck rotation and torsional damage to the columns of the bridge. The study in hand assumes the deck of the curved bridge as a completely rigid body to analyse the multi-body oblique frictional impact at the deck-abutment interaction. Extending other authors' work, a linear complementarity formulation is implemented for computing the unilateral contact to identify the effects of different impact states, such as stick and forward or backward slip, depending on the initial conditions during single or double impact. Stick and slip conditions during single impact are evaluated for different pre-impact rotations and ratios of transverse to normal pre-impact relative velocities. Also, the inward and outward slips during double impact, which represent the possibility of the deck being out-off lane, and the possibility of post-impact deck rotation are estimated for several curved geometries. The results show the curved bridge is very susceptible for in-plane deck rotation and out-off lane misalignment during the deck-abutment pounding.