Abstract: A computer program has been developed for calculating the phase diagrams of predominance areas (LOGPo₂-LOGPs₂, LOGPo₂-LOGPso₂ diagrams) by the use of the method of linear programming. The concrete equilibrum relationships of thermodynamics between substances in the LOGPo₂-LOGPs₂, LOGPo₂-LOGPso₂ diagrams has been described mathematically and all the problems of thermodynamics have been changed to the problems of linear programming completely, The general computer program of the calculation for the LOGPo₂-LOGPs₂, LOGPo₂-LOGPso₂ diagrams has been written by the use of the Revised Simplex Method which is employed for the computer to solve the problems of linear programming. This method is considerably simpler, more clear and reliable in mathematical model than previously reported methods and make use of the method of linear programming to determine the predominance areas of substances.