One of the most common ignition mechanisms for the ignition of nonmetallic materials in an oxygen system is rapid compression. Energy from the rapid compression process is transferred from the hot gaseous oxygen to an adjacent nonmetallic material, which leads to temperature rise and ignition. The development of a mathematical model that simulates the thermal condition of the nonmetal ignition when subjected to a rapid compression is presented. A material's autoignition temperature was initially used as a criterion for the occurrence of ignition. The model developed can be used to predict the rise in the temperature profile of any nonmetal. The significance of this research is to improve fire safety within oxygen systems by establishing a theoretical model to reduce, or mitigate, the occurrence of rapid compression.