This work has a theoretical and computational character, whose objective is the study and application of an optimization technique for the solid-liquid equilibrium calculation. Focused on binary and ternary fatty mixtures with natural origin, this work can also be applied for different mixtures of fatty acids, triglycerides and ethyl esters using the minimization of Gibbs Energy of the systems. This problem was formulated as a non-linear program, and convexity analysis ensured that the optimal solution found was the global optimum. The equilibrium problem was implemented in software GAMS in addition of Microsoft Excel, where the description of phases was done based on two thermodynamic models. The solid phase was characterized using a modified Slaughter and Doherty model, while the liquid phase was modeled with Margules 2 – suffixes and the Wilson Model. In the liquid phase, the Margules model assumes two forms: Margules Asymmetric, where the Margules parameters are different, and Margules Symmetric, with equal Margules parameters. In this work specifically, it was calculated the equilibrium points with some combinations of myristic, palmitic and capric acids; ethyl laurate, miristate and palmitate; tripalmitin and tristearin was calculated. Experimental data was used in comparative mode of binary mixtures, with good agreement between experimental and calculated points; new equilibrium data were predicted and obtained for ternary mixtures, and the parameters model also was determined. The results were described in the form of phase diagrams for binary mixtures and surfaces of equilibrium for ternary mixtures, where the equilibrium data and the parameters model were calculated based on the square errors, and fitted well to the experimental data.