Single crystal diamond has the highest hardness, high elastic modulus and good antiwear and anticorruptibility. Today, there are many industrial applications of single crystal diamond, including single point cutting, aircraft window, and many others science and technology fields. With the development of applying field, precise surfaces are required. But due to its especial physical properties of diamond, it is difficult to be lapped. So it has good application future to do researches on precise lapping of diamond.Firstly, the elastic float lapping based on elastic system is presented. When the diamond and the lapping plate are in elastic system and the elastic parameters are designed and selected, it can decrease the bad elements and get precision diamond surface. Based on this principle, the experimental equipment was designed and rebuilt. The lapping traces were controlled by computer. The results show this method can get a high precision of diamond surface. Based on the experiments, the characteristics of elastic lapping were also studied.Three different lapping regions, including crater area of diamond surface, dissociation area and smooth area, were observed during diamond lapping process by elastic float lapping. Those three regions correspond to three different lapping processes. The studies on how those regions come into being were carried out. The studies show that when a diamond was lapped in rough lapping plate, the removal mechanism of diamond is result from machine removal. With the evolution of lapping, the material of diamond is equably removed in elastic float lapping. And a precise diamond surface can be got.In this paper, the effects of lapping speed and elastic coefficient on the quality of diamond surface are discussed. The results show that the changes of parameter affect the quality of surface. The results show that n =l80rpm and K=13.2N/mm is good for diamond lapping.Finally, a vibration test on elastic system, which attenuates and separates vibration, was done. Based on the tests, the effect of surface impact on the surface quality is analyzed and a model of elastic float lapping was established.