A mathematical model is proposed describing the process of wetting the walls of a cylindrical body by a metallic melt and the subsequent formation of a meniscus. An aluminum alloy cup located on an aluminum oxide substrate was selected as the object of modeling, for which the dynamics of the flow of molten solder metal during wall wetting under various gravity conditions was studied. The calculations are performed in an isothermal setting when the system temperature exceeds the melting point of the solder. Based on the calculation results, the shape of the meniscus is analyzed, and the equilibrium position of the meniscus boundary on the sample surface is predicted. Additionally, the issue of the limiting contact angle of wetting, which ensures that the melt flows into the inner volume of the glass, is investigated, which is important for the development of soldering technology for parts with a complex interface surface.