In the present work second order mathematical models for semifinish honing are presented for average roughness Ra as a function of abrasive stone characteristics and honing parameters. Several tests were performed in both a test machine and in an industrial machine. Results from both machines were compared. Although roughness depends on the five variables studied (grain size, density, pressure, linear speed and tangential speed) in both cases, most important factors are grain size and pressure. It is possible to use the model for the test machine in the industrial machine, in a way that only a few tests will be performed in the industrial machine in order to translate the model.