This work analyzes the spreading of a flame originating at the surface of a polymeric solid. Such combustion process is controlled by a number of factors, in particular by the thermodynamic state of the solid and that of the incoming gases. By identifying the range of properties in which the rate of spread is enhanced, substances and wall geometries to be avoided in fire resistant structures can be identified. Realistic shapes and chemical kinetics demand detailed numerical calculations for which the NSF supercomputer network is well suited. Understanding the effect of polymeric materials and product shape on flame spreading will give a valuable insight to the designers of fire-resistant structures. Accurate predictive methods will replace present uncertainties in the design of a wide range of products (furniture, plastic moldings, paints, etc.).