Recent experimental measurements of soot volume fraction in a flickering CH4/air diffusion flame show that for conditions in which the tip of the flame is clipped, soot production is similar to 5 times greater than that measured for a steady flame burning with the same mean fuel flow velocity (Shaddix et al., Ref. 9). This paper presents time-dependent numerical simulations of both steady and time-varying CH4/air diffusion flames to examine the differences in combustion conditions which lead to the observed enhancement in soot production in the flickering flames. The numerical model solves the two-dimensional, time-dependent, reactive-flow Navier-Stokes equations coupled with submodels for soot formation and radiation transport. Qualitative comparisons between the experimental and computed steady flame show good agreement for the soot burnout height and overall flame shape except near the burner lip. Quantitative comparisons between experimental and computed radial profiles of temperature and soot volume fraction for the steady flame show good to excellent agreement at mid-flame heights, but some discrepancies neat the burner lip and at high flame heights. For the time-varying CH4/air flame, the simulations successfully predict that the maximum soot concentration increases by over four times compared to the steady flame with the same mean fuel and air velocities. By numerically tracking fluid parcels in the flowfield, the temperature and stoichiometry history were followed along their convective pathlines. Results for the pathline which passes through the maximum sooting region show that flickering flames exhibit much longer residence times during which the local temperatures and stoichiometries are favorable for soot production. The simulations also suggest that soot inception occurs later in flickering flames, and at slightly higher temperatures and under somewhat leaner conditions compared to the steady flame. The integrated soot model of Syed et al. (Ref. 12), which was developed from a steady CH4/air flame, successfully predicts soot production in the time-varying CH4/air flames.