An integrated theoretical/numerical framework is established to study the erosion of graphite nozzle material in solid rocket motor environments. The model takes into account propellant chemistry, detailed thermofluid dynamics, chemical kinetics in the gas phase, heterogeneous reactions at the nozzle surface, and nozzle material properties. The gas-phase flame dynamics is based on the complete conservation equations for multi-component reacting system. Typical combustion species of AP/HTPB propellant at practical motor operating conditions are considered at the nozzle inlet. Full account of variable transport and thermodynamic properties is considered. Turbulence closure is achieved using a two-layer turbulence model, which employs the standard k-ε two-equation approach for the bulk flow away from the wall (i.e., the outer layer), and a single k equation in the near-surface region (i.e., inner layer). The energy equation is solved for the process in the nozzle material with appropriate species and energy boundary conditions at the gas-solid interface. Two heterogeneous reactions involving graphite and the oxidizing species of H2O and CO2 are considered at the interface. The predicted surface recession rates compare well with available experimental data. The results indicate that erosion is most severe at the nozzle throat. The important factors that dictate the erosion process are nozzle surface temperature, rate of diffusion of oxidizing species towards the surface, and motor operating conditions. The erosion rate increases with increasing chamber pressure and can be correlated using a power law. The erosion also becomes more severe with propellants with decreased aluminum content.