The burning behavior of polyethylene in the counterflow of oxidizing air has been studied numerically with a coupled model describing feedback heat and mass transfer between gas-phase flame and polymeric solid fuel. A 2-dimensional elliptic equation in axisymmetric formulation (revealing the cylindrical shape of the polymer sample used in the experiment) has been employed to simulate heat transfer in solid fuel, and a set of 1-dimensional hyperbolic equations has been used to determine the solid-to-gas conversion degree of the pyrolysis reaction. Four sets of products compositions and two modifications for the kinetic parameters of solid fuel pyrolysis reaction have been taken into account. Gas-phase formulation is presented by set of 1-dimensional conservation equations for multi-component flow with detailed kinetic mechanism of combustion. The profiles of temperature and species concentrations in the flame zone have been calculated and compared with the results of experimental study of combustion of ultrahigh molecular weight polyethylene. Higher hydrocarbon composition (dodecane) has been found to show the best agreement between the temperature and species concentration profiles with the measurements, especially for the low-level mass fractions of the by-product components-propylene, butadiene, and benzene.