The success of gas reactors depends upon the safety and quality of the coated particle fuel. The fuel performance modeling code PARFUME simulates the mechanical, thermal and physico-chemical behavior of fuel particles during irradiation. This report documents the theory and material properties behind various capabilities of the code, which include: 1) various options for calculating CO production and fission product gas release, 2) an analytical solution for stresses in the coating layers that accounts for irradiation-induced creep and swelling of the pyrocarbon layers, 3) a thermal model that calculates a time-dependent temperature profile through a pebble bed sphere or a prismatic block core, as well as through the layers of each analyzed particle, 4) simulation of multi-dimensional particle behavior associated with cracking in the IPyC layer, partial debonding of the IPyC from the SiC, particle asphericity, and kernel migration (or amoeba effect), 5) two independent methods for determining particle failure probabilities, 6) a model for calculating release-to-birth ratios of gaseous fission products that accounts for particle failures and uranium contamination in the fuel matrix, and 7)