In this paper we present an extension of the statistical associating fluid theory (SAFT) for branched molecules with a Lennard-Jones dimer reference fluid (SAFTD-LJ-Branch). The theory successfully predicts how branched architecture affects the attraction and repulsion between molecules. SAFTD-LJ-Branch takes a form similar to SAFTD-LJ with an additional parameter NB introduced to account for the branching effect. We propose an approach relating NB to the number of different types of articulation segments. The theory is used to study the effect of chain architecture on the thermodynamic properties of isomeric alkanes. SAFTD-LJ-Branch accurately predicts the phase diagram of pure butane, pentane or hexane isomers. Further, vapor pressures of n-triacontane and squalane are predicted without further fitting and shown to be in semiquantitative agreement with experimental data. Finally, SAFTD-LJ-Branch is demonstrated to be well applicable to mixtures as we model the vapor-liquid coexistence of binary alkane mixtures containing different hexane isomers and recover the experimental trends.