In most internal combustion engines and reciprocating compressors, thin-walled plain bearings are generally used. When designing an engine bearing unit, it is rational to take a hierarchical approach (from the simple to the complex) in order to select a mathematical model. In such cases, a one-dimensional mathematical model is often used as the first step. In the article, it is proposed to use the results of approximation of graphical dependencies in the form of analytical dependencies (dependency of relative eccentricity on bearing load factor, dependency of oil volume flow coefficient on relative eccentricity). Using approximating functions, a specification calculation of the sliding bearing for the high-speed small-sized air-cooled diesel engine 1 Ch 8.0/7.5 (single-cylinder four-stroke) was performed. The calculation was simplified by means of approximating functions to allow for the automation of the calculation (by connecting the corresponding module to the previously developed system of automatic design of diesel engine). © 2021, Springer Science+Business Media, LLC, part of Springer Nature.