A 3-D finite-element model was used to simulate the severe and localized thermal/pressure transients and the resulting stresses experienced by a rifled ceramic liner with a steel sheath. The focus of the simulations was on the influence of the rifling fillets on the heat transfer and resulting thermoelastic stresses (including pressure transients) generated during a single firing event. Since the modeling was primarily concerned with the effects of the rifling groove, a small, twisted segment of the barrel length based on rotational symmetry was employed. Using this simplification, the model utilized uniform heating and pressure across the inner surface via a time-dependent convective coefficient and pressure generated by the propellant gasses. Results indicated that the inner fillet radius of the rifling groove (rf2) had the greatest influence on the maximum circumferential (hoop) stresses and temperatures experience by the rifled barrel. Based on these simulations, it is recommended that rf2 be kept as large as possible in order to reduce the tensile hoop-stresses. Moreover, it appears to be permissible to keep the outer fillet radius of the groove (rf1) relatively small so as to help ensure that the rifling will adequately engrave the projectile and transmit rifling torque.