In the present work a mathematical model for the simulation the APCI C3MR process for natural gas liquefaction, in two vapor compression refrigeration stages, is presented. In the first stage, with propane as the working fluid, the temperature of natural gas is reduced to -35 ºC. The second stage uses a mixture of nytrogen, methane, ethane and propane as refrigerant. The evaporators of the pré-cooled cycle are used as condensers for the liquefaction cycle. The mathematical model is formed by the mass and energy conservation equations, applied to adequate control volumes, and by the thermodynamic properties equations, from the computational package REFPROP, developed by NIST, USA. A computational program was developed in platform EES, to solve the resulting non-linear system of algebraic equations. As input for the program, data from an existing NG liquefaction plant in Pampa Mechorita, south of Lima, Peru, were used.