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Proposed is an algorithm for calculating heat and mass transfer in electrothermal ore recovery processes in non-ferrous metallurgy. To implement the algorithm, the finite element method was used, which allows to take into account complex configuration of the internal volume of the reactor. A finite element grid automatic construction algorithm was used. An iterative algorithm for the finite element equations implementation with the matrix width optimization and the use of symmetry properties is proposed. A set of programs that allows to calculate operating modes of electrothermal ore-smelting reactors of any design, including those used in the smelting of non-ferrous metal alloys, has been developed. The interface of the programs is user-friendly. The multi-document interface provides visualization of the calculation results in the form of isolines of temperature fields and velocity vectors.