The present study presents theoretical analysis of an engineering mixed lubrication contact in one-dimensional case between a deformable plane of regular roughness and an ideally smooth rigid plane. The roughness of the plane, respectively take the forms of triangle and truncated triangle ridges which are evenly distributed on the plane surface. The rough plane is assumed as elastic-plastic. The contact between the tip of the ridge on the plane and the other smooth plane is assumed as in dry contact or oxidized chemical boundary layer contact, while the regions between other parts of the ridge and the smooth plane are, respectively in physical adsorbed boundary layer contact and continuum film hydrodynamic contact. The lubricant in the continuum film hydrodynamic contact is assumed as Newtonian. The whole contact between these two planes is obtained by periodically distributing the ridge on the plane. Theoretical analysis are developed for this mode of contact, respectively for triangle and truncated triangle surface ridges for wide operational parameters when the plane ridge, respectively undergoes elastic and plastic deformations and the hydrodynamic contact areas between the planes are varied. The present study demonstrates the theoretical analysis. In the following parts will be demonstrated the results obtained from the present analysis.