An approximate analytical model has been developed to obtain simultaneous solutions for nonlinear solute- and heat-transfer equations for multi-component alloy steels; in this model, a linear relation between the solid fraction and the temperature in the mushy zone was assumed. This model predicts important parameters, such as the solidus temperature for the multi-component steel materials that have not been well confirmed by the reliable measurement in a real process. The predicted temperature, solidification constants, and effective partition ratios of solutes were in good agreement with both the reported measurements and generally accepted values. The predicted solidus temperatures were also in reasonable agreement with the reported zero ductile temperature of Fe-C-Mn steel and the thermo-analytically measured solidus temperatures of steels of various grades. The solutions were also in good agreement with those separately performed numerical thermal analysis. The model involves the solution for Fe-C binary alloy which is consistent with the Neumann's solution in the low carbon range. Thus, this model provides approximate analytical solutions that can reduce the computational load, saving time and cost. (C) 2018 Elsevier Ltd. All rights reserved.