An important aspect of studying soil behaviour under seismic loading is the accurate modelling of time-dependent and random seismic forces. The pseudo-static method of analysis is very approximate and although the pseudo-dynamic method considers phase difference and amplification effects, it has certain limitations. The modified pseudo-dynamic method considers the time-dependent behaviour of seismic forces and inherently accounts for the amplification of acceleration, thus making it more realistic. This newly developed method is applied to determine seismic inertia forces for estimating the seismic bearing capacity factor (N_γe) of dry sand underlying shallow strip footings. Limit equilibrium approach is used and a one-sided composite failure surface is considered to be developed under seismic load. The focus of the log-spiral is iteratively determined to give the least value of N_γe. The results are presented graphically in non-dimensional form which may be used by geotechnical practitioners for design in seismically active regions.