A theoretical study of the elastohydrodynamic lubrication (EHL) of line contacts with couple stress fluids as lubricants is presented. The paper mainly deals with the theoretical values of the central film thickness within the elastic contacts of rolling and sliding surfaces in terms of equivalent radius of a cylinder and a plane. The central film thickness is numerically calculated based on Grubin's theory of inlet builtup pressure and considering the effect of a couple stress parameter in complex fluids. In particular cases, film thickness and pressure distribution are also numerically calculated and graphically presented by considering the cavitation boundary condition. A comparative study of the couple stress behavior with the Newtonian behavior of lubricants has been made. As per experimental studies, the central film thickness in EHL contacts depends on a variety of lubricants under identical operational conditions. The present theoretical consideration with couple stress fluid indicates that the presence of a couple stress parameter increases the central film thickness in EHL contacts lubricated with complex fluids, e.g., polymeric and synthetic lubricants.