This paper discusses rough surfaces contact phenomena and in particular examines surfaces machined with abrasive instruments. The nature of surface roughness obtained as a result of this type of mechanical treatment can be described by the random field of two variables. Attention is paid to three-dimensional surface roughness parameters whose statistical characteristics are determined by the simple rough surface model: for an anisotropic random field obtained by mathematical stretching of an isotropic random field. Consideration is given to surface contacts: rough and smooth surface interaction and the contact of two rough surfaces. Two types of asperities contact are examined: plastic and elastic. The criteria for contact type have been developed. Contact theory is used for the calculation of contact resistance in welding and of wear intensity. The equations obtained reveal that all of them contain one surface roughness height parameter and two spacing parameters.