Based upon a slip-line analysis of the plastic deformation of surface asperities, a theory is developed determining the Ra-value (c.l.a.) and the average effective strain in the surface layer when deforming asperities in metal-working processes. The ratio between Ra and Ra0, the Ra-value after and before deformation, is a function of the nominal normal pressure and the initial slope γ0 of the surface asperities. The last parameter does not influence Ra significantly. The average effective strain View the MathML sourcege in the deformed surface layer is a function of the nominal normal pressure and γ0. View the MathML sourcege is highly dependent on γ0, View the MathML sourcege increasing with increasing γ0. It is shown that the Ra-value and the strain are hardly affected by the normal pressure until interacting deformation of the asperities begins, that is until the limit of Amonton's law is reached. After that Ra decreases and the strain increases rapidly with the normal pressure, Ra approaching zero whilst View the MathML sourcege approaches a limiting value depending on the initial slope of the asperities.