Theory and computer simulations of model polymers are presented. Polymers are modeled as freely-jointed beads, with the nonbonded bead-bead interactions given by the Lennard-Jones potential; a harmonic spring potential is used for the bonding interactions. Simulation results for linear chains containing 200 beads are presented. A thermodynamic perturbation theory for polymerization is compared to simulation data for chains containing from two to 200 beads, over a range of temperatures and densities. Two variations of the theory are investigated, one utilizing a reference fluid of monomers (TPT1-M), and another employing a dimer reference fluid (TPT1-D). It is found that TPT1-D is far more accurate for predicting the pressures of linear flexible chains than TPT1-M. At low densities TPT1-M predicts internal energies that are too high compared to simulation data. This is because TPT1-M neglects intramolecular contributions to the configurational energy. TPT1-D gives a more accurate description of the low density energies of flexible chains by incorporating structural information about the dimer fluid into the reference term. Computer simulations of ring polymers are presented. Noninterlocking flexible rings with 3, 8, and 20 beads are modeled. Simulations of rigid planar rings containing 3 and 8 beads are also presented. Pressures and energies for rigid and flexible 3-mer rings are virtually identical, even though the flexible model includes bond vibrations which are absent in the rigid ring model. In contrast, the pressure of the rigid 8-mer ring fluid is always higher than the pressure of flexible ring fluids at the same temperature and density. Extensions of TPT1-M and TPT1-D for ring polymers are compared with simulation results for flexible and rigid rings. The monomer reference theory predicts pressures that are too high for flexible rings but too low for rigid 8-mer rings at high densities. TPT1-D for rings gives good agreement for pressures and energies of flexible rings at high densities, but incorrectly predicts a two-phase region for ring polymers at supercritical temperatures.