This research deals with the influence of the surface roughness on the friction properties for a hard hemispherical projection of the radius of curvature r sliding on a smooth soft surface or a soft one with the hemispherical projections of the radius of curvature R. This paper is examined on the effects of various factors on the relationship between the indented depth and the friction coefficient. The friction mechanism between the hard hemispherical projection of the radius of curvature r modeled on the asperity of a hard material surface and the soft surface has been theoretically analyzed taking into consideration with the frictional resistance caused by the ploughing and shearing term. The results of numerical examples based on theoretical analysis can be expressed as follows. The friction coefficient for the smooth soft surface increases with the increase of a contact angle that obtains from the radius of curvature r and an indented depth λh of the hemispherical projection.