In the lapping of magnetic heads and other electronic components composed of multiple materials, differences in the processing characteristics of the composite materials result in “residual steps” forming on the surface at composite interfaces. Residual step heights have been reduced to as little as a few nanometers. We investigated using fine abrasives in fixed abrasive lapping for this purpose, which requires highly secure, high-density embedding of the abrasives on the lapping plate. To this end, we modeled the abrasive embedding process and investigated the relationship between the mechanical properties of the lapping plate and the retention of the abrasive, to determine the direction of further research and development. The results of this investigation revealed a correlation between the work hardening in the plate and the resulting abrasive density and cutting edge height. The investigation also showed that it is possible to suppress the reduction in lapping rate that occurs during use by increasing the work hardening coefficient of the plate.