We have considered the issues of how structural characteristics of grinding discs influence the roughness of the processed workpiece surfaces. The analysis of the known research about dependences of roughness parameters of polished surfaces on the disc grit, hardness and structure has been given. The technique to determine the optimum disc hardness which is boundary on the maximum value of the roughness parameter has been demonstrated. The functional dependences of the roughness parameter R a on the disc structure characteristics, the cutting mode and the processing conditions have been established for flat, round external and cutin grinding.