Geometric, energy, and impulse models were developed to study the interaction of the abrasive and the ground surfaces in finishing. The geometric and energy models describe the process of finishing in the case of the use of tools with a fastened abrasive. The impulse model reflects the real picture of the action of unfastened abrasive grains on the surface being ground. The spectral density of the input signal is determined. The weight function and transfer function are treated. The spectral theory of the linear transformation of the stationary random function is used. On the basis of the experimental data and theoretical solutions, equations are obtained with which it is possible to predict the changes in surface roughness for various abrasive particle sizes.