Predictions of critical lines and partial miscibility of binary mixtures of hydrocarbons have been made by using a modified version of the statistical associating fluid theory (SAFT). The so-called soft-SAFT equation of state uses the Lennard-Jones potential for the reference fluid, instead of the hard-sphere potential of the original SAFT, accounting explicitly for the repulsive and dispersive forces in the reference term. The mixture behavior is predicted once an adequate set of molecular parameters (segment size, dispersive energy, and chain length) of the pure fluid is available. We use two sets of such parameters. The first set is obtained by fitting to the experimental saturated liquid density and by equating the chemical potential in the liquid and vapor phases for a range of temperatures and pressures. The second set is obtained from the previous one, by rescaling the segment size and dispersive energy to the experimental critical temperature and pressure. Results obtained from the theory with these parameters are compared to experimental results of hydrocarbon binary mixtures. The first set gives only qualitative agreement with experimental critical lines, although the general trend is correctly predicted. The agreement is excellent, however, when soft-SAFT is used with the rescaled molecular parameters, showing the ability of SAFT to quantitatively predict the behavior of mixtures. The equation is also able to predict transitions from complete to partial miscibility in binary mixtures containing methane.