In floating lapping with solid abrasives, the workpiece is taken as an isolated body. The forces that act on it are analyzed. A differential equation about the forces that act on it is set up, so the forces that act on it and its motion rule are received. Combining it with known lapping tool motion, the relative motion rule between the lapping tool and workpiece is determined too. According to the relative motion, the distribution of abrasives density is designed reasonably, which makes the lapping tool wear uniformly, which, in turn, avoids redressing the lapping tool, saves abrasives, and increases machining accuracy. Combining it with advantages in high speed lapping with solid abrasives, the low cost, high efficiency nanometer lapping at high speed is realized.nanometer machining, high speed lapping, solid abrasives, force analyzing With science and technology advancing and society progressing, the requirements for machining accuracy increase. Thus machining technology level is raised. Nanometer machining technology has been developed from precision machining and ultraprecision machining technology. There are two disadvantages in present nanometer machining technology: low machining efficiency and high machining cost. Both limit nanometer machining technology used widely. This paper discusses nanometer lapping using solid abrasives at high speed with high efficiency and low cost.