A statistical mechanical based model for simultaneously calculating liquid and gas phase viscosities using the square well intermolecular potential has been developed. Theoretical results are utilized along with modifications to correct the model for the molecular chaos assumption and the inadequacy of the square well potential. The radial distribution function values are determined from perturbation theory. Model parameters are obtained from liquid and gas viscosity data and generalized with group contributions. With the resulting model, liquid and gas viscosities of a variety of nonpolar compounds are correlated within 5% and 3%, respectively, and predicted within 8% and 5%, respectively.