A new integral thermal pyrolysis model for the transient pyrolysis of charring and on-charring materials has been developed and evaluated by comparison of the results with exact solutions. The purpose for the development of this simple model has been the desire for predicting pyrolysis histories of materials exposed to pre heat fluxes by using “equivalent” properties tailored to the present model and common flammability test measurements. The pyrolyzing material is divided into a char layer and a unpyrolyzed (virgin) layer where the material has not yet pyrolyzed. These two layers are separated by an isothermal interface which is at a pyrolysis temperature (characteristic of the material). At this interface, heat is transferred to the virgin layer, causing further pyrolysis of the material (namely a thermal pyrolysis model is used). A one-dimensional transient heat conduction model is used to predict the heat transfer within the material. Exponential temperature profiles were assumed for the heat conduction model. Using a rwo-equation 9-moment method, the original partial differential equations were transformed into a set of two ordinary differential equations for each layer. These equations were numerically salved to I) determine the pyrolysis rate. regression depth and surface temperature, and 2) establish a dimensional and sensitivity analysis. The model has been shown to be very accurate (errors ~ 2%) from comparisons between numerical results and exact solutions. Despite the neglect of derailed chemical kinetic (Arrhenius) pyrolysis expressions, the accuracy of the integral model together with its simplicity has allowed the deduction of pyrolysis properties of materials by using common flammability test data as it ';ill be proved in a subsequent paper.