Quantitative understanding of the processes that take place inside a burning material is critical for the prediction of ignition and growth of fires. To improve this understanding and enable predictive modeling, we developed a numerical pyrolysis solver called ThermaKin. This solver computes transient rate of gaseous fuel production from fundamental physical and chemical properties of constituents of a pyrolyzing solid. It was successfully applied to the simulation of combustion of a broad range of materials. One limitation of ThermaKin was that it could handle only one-dimensional burning problems. As a consequence, flame spread, which is an important contributor to fire growth, could not be simulated. Here, we present a new computational tool, ThermaKin2D, that expands ThermaKin model to two dimensions and combines it with a flexible analytical representation of a surface flame. It is our expectation that this tool will enable highly accurate simulations of flame spread dynamics. This manuscript contains a description of this new computation tool, reports results of a series of verification exercises, and demonstrates some of the ThermaKin2D's capabilities. Published 2013. This article is a U.S. Government work and is in the public domain in the USA.