A chemical kinetic model for the thermal decomposition of the solid high explosive pentaerythritol tetranitrate (PETN) is developed for prediction of times to thermal explosion using the Chemical TOPAZ heat transfer computer code. The model is based on times to thermal explosion measured in a new One Dimensional Time to Explosion (ODTX) apparatus. ODTX experiments are reported for pure PETN and for Semtex 1A. The pure PETN results are accurately modeled using a four reaction decomposition process in which an autocatalytic process produces intermediate reaction product gases, which subsequently react in a second order gas phase process to produce the final reaction products. Semtex 1A exhibits longer times to explosion than PETN at low temperatures, indicating that its endothermic binder decomposition absorbs heat produced by PETN decomposition. This binder reaction is modeled as a first order endothermic process. Three experiments on 5.08 cm diameter unconfined cylinders of PETN ramp heated to explosion at different rates are reported. The PETN model accurately predicts the thermocouple records and explosion times for these unconfined experiments in which only intermediate gaseous products can form.