A blast furnace is a complex metallurgical unit, which is characterized by a significant delay and inertia in the processes of heat and mass transfer. Therefore, an important issue in solving technological problems for controlling blast furnace smelting and improving the operating modes of a blast furnace is the research of transient processes. The slag mode of blast furnace smelting determines the most important technical and economic indicators of a blast furnace, such as the specific consumption of coke and productivity. The composition of the slag, its specific gravity and properties affect the gas-dynamic, thermal and reduction processes taking place in the blast furnace. A description of the algorithm for modelling transient processes in the composition and properties of the final slag is presented. The algorithm includes the calculation of a set of parameters characterizing the composition and properties of the final slag (the content of the main components, the basicity and the viscosity of the slag at different temperatures). It takes into account the change in the consumption and chemical composition of iron ore materials and fluxes, the consumption and technical composition of coke, and the composition of coke ash. Based on the algorithm, a software module has been developed and variants for solving the problems of calculating transient processes in the composition and properties of the final slag of a blast furnace are presented.