The peak storey drift demands that an earthquake imposes on a building can be assessed through a detailed engineering seismic assessment or recorded if a building is instrumented. However, for the rapid seismic assessment of a large number of buildings, it is desirable to have a simplified means of estimating storey drift demands. Consequently, this paper proposes a simplified means of quickly estimating storey drift demands on reinforced concrete (RC) frame buildings. Expressions for peak storey drift demand as a function of ground motion intensity are developed by utilising concepts and simplifications available from displacement-based seismic design and assessment methods. The performance of the approach is gauged by comparing predicted storey drift demands with those obtained from rigorous non-linear time-history analyses for a number of case study buildings. The promising results suggest that the approach proposed will be useful for rapidly assessing the likelihood of damage to a range of drift-sensitive elements in modern RC frame buildings.