<p>In engineering and industrial applications, the stability of a lubricant is enhanced by adding different commercial additives, such as Polyisobutylene, Ethylene-propylene, lithium hydroxy stearate, and hydrophobic silica. These additives change many rheological properties of the base lubricants and force them to behave like pseudoplastics and dilatants. These lubricants can be precisely described using the Sisko fluid model. This theoretical study examines the impact of non-Newtonian pseudoplastic and dilatant lubricants on the squeezing behavior between two cylindrical surfaces. The analysis involves deriving of a modified form of the Reynolds equation and obtaining a closed-form solution for film pressure. Numerical values of film pressure, load-carrying capacity, film response time, and coefficient of friction have been calculated and analyzed for different values of material parameter and flow index. The analysis shows that the squeezing characteristics are significantly influenced by the non-Newtonian pseudoplastic and dilatant properties of the lubricants. It has been observed that in comparison to base lubricants, dilatant lubricants increase the film pressure and load capacity of the system with a longer response time, while pseudoplastic lubricants produce lower film pressure and load capacity with a shorter response time. Overall, the additives enhance the stability and life of a bearing.</p>