We present results for the solid-fluid phase equilibrium for molecular models of chain molecules using Monte Carlo computer simulation and cell theory. We were concerned primarily with the role of molecular shape and flexibility on the solid-fluid phase equilibrium. We have considered models with different intramolecular potentials to examine the effect this has on the phase diagram. Extensive calculations of the fluid and solid phase equations of state have been made and solid phase free energies have also been determined. Our results for the fluid properties are compared with various theoretical equations of state which have been proposed for these systems. A method for calculating the solid phase free energy of chain molecules has been developed based on finding a reversible path to an Einstein crystal. For models of freely jointed chains of tangent hard spheres, the dependence of the solid phase thermodynamics upon the chain conformation has been studied and solid-fluid phase diagrams for chains with lengths ranging from three through eight atoms have been determined. In the case of models of flexible united atom chains, solid-fluid phase diagrams for chains with lengths ranging from four to eight atoms have been determined for three different torsional potentials. The data for flexible united atom chain models have been used as reference systems in a generalized van der Waals or mean field calculation of the n-alkane phase diagrams. This theory reproduces trends in the triple point temperature seen in experimental data. These trends are interpreted in terms of the changes in the close packed densities of the solids with chain length and the effect of the torsional energy on the relative stability of the fluid and solid phases. A cell theory was developed that was applicable to the flexible hard sphere site united atom model. The theory was in good agreement with the Monte Carlo simulations. Finally the phase diagram of a flexible united atom model mixture was determined. The model phase diagram showed that a solid-solid mixture phase coexistence can occur in these systems. However the method for calculating [special characters omitted] a required quantity was not accurate enough to definitively calculate the phase diagram. The data showed clear overall trends that the value of [special characters omitted] at constant pressure decreased with increasing mole fraction and that as the pressure increased the slope of [special characters omitted] versus mole fraction increased. These trends were present for the two different system sizes considered.