As a result of the numerical investigation of a typical polymeric material ignition by a local energy source with limited heat content it has been determined three modes: gasification without ignition followed by pyrolysis stop, stable ignition, and unstable ignition. The mathematical model of the process takes in account conductive heat transfer and thermal decomposition in condensed phase, diffusion-convective heat and mass transfer and gaseous pyrolysis products oxidation of polymeric material in air