The process of abrasive machining in lapping is considered as a moving sharp indentor subjected to normal force and tangential force. Based on indentation fracture mechanics theory, the grinding stresses of material, the location of median crack initiation and the direction of median crack propagation beneath an abrasive are analyzed. The calculation formula of median crack propagation length is analyzed by synthetically considering the contribution of elastic stress field, residual stress field and tangential force beneath the abrasive. A theoretical model of relationship between subsurface damage and surface roughness is established. A method of magnetorheological finishing (MRF) spot technique is proposed to the depth of subsurface damage. Predicted results are compared with experimental results, result shows that the error between predicted results and experimental results is less than 5.56%. The theoretical model can be used for prediction the depth of subsurface damage of optical materials in lapping process rapidly, expediently and accurately.