Recently, wheel separation accidents in such vehicles as trucks, buses and passenger cars have drawn a social concern. Explications of their causes and adequate practices of countermeasures for them have been urgently required. In relation to this issue, the authors have taken notice of subjects which are concerned in bolted joints at wheels and are especially trying to study the pressure distribution at the bearing surface of nuts. This report deals with the subject of a nut with a cone-form bearing surface. Considerations are based on numerical results derived from finite-element-analysis. Feature of the pressure distribution by this profile and influences from geometrical deviations of the form are mainly discussed, and some other information concerning this issue is presented.