Even if precast pre-stressed hollow-core (PPHC) slabs are usually designed as simply supported elements, continuity with the supporting beam may exist when constructed together with a reinforced concrete topping and continuity reinforcing bars. During an earthquake (and possibly other lateral load), this continuity may result in bending moments being induced close to the supports as the buildings sway laterally. The response of precast floors to earthquake-induced demands has been addressed by past research. However, further investigation is required to improve understanding of several aspects of precast floor behaviour either revealed or emphasized by recent earthquakes in New Zealand. This paper proposes a mechanics-based modelling approach for the analysis of PPHC slab-to-beam seating connections. The model has been calibrated against existing test data to predict the failure of a PPHC slab under negative bending moments. The numerical outcomes allow comparison of the moment–drift response, principal tensile stresses, and crack progression during loading. The developed modelling approach will allow future studies to exhaustively investigate all aspects of precast floor behaviour by varying the properties and geometry of the PPHC seating connection.