The calculation of transport properties of solids is of vital importance in the engineering practice. This paper is focused on the development of a mathematical model for the calculation of the thermal conductivity for simple solids with the help of statistical mechanics. Contrary to classical mechanics, the use of statistical theories provides an insight into the world of atoms and molecules (a microscopic description of phenomena). The observation of the phenomena of molecules and atoms enables us to calculate all thermomechanical properties of state of the macroscopic world. The Eliashberg coupling function was used for the calculation of electronic contribution. New constants for some metals were obtained with the presented model. The analytical results obtained by statistical mechanics are compared with the experimental data and show a relatively good agreement.