Flame spread over solid fuels with simple geometries has been extensively studied in the past, but few have investigated the effects of complex fuel geometry. This study uses numerical modeling to analyze the flame spread and burning of wavy (corrugated) thin solids and the effect of varying the wave amplitude. Sensitivity to gas phase chemical kinetics is also analyzed. Fire Dynamics Simulator is utilized for modeling. The simulations are two-dimensional Direct Numerical Simulations including finite-rate combustion, first-order pyrolysis, and gray gas radiation. Changing the fuel structure configuration has a significant effect on all stages of flame spread. Corrugated samples exhibit flame shrinkage and break-up into flamelets, behavior not seen for flat samples. Increasing the corrugation amplitude increases the flame growth rate, decreases the burnout rate, and can suppress flamelet propagation after shrinkage. Faster kinetics result in slightly faster growth and more surviving flamelets. These results qualitatively agreement with experiments.