In this work, the pyrolysis and ignition of thermally thick poly (methylmethacrylate) material with low periodic on-off irradiation was investigated, the solid and gas absorption was ignored, an ignition time formula with periodic heating was established based on the deduced ignition time model. The results show that the surface and in-depth sample temperatures as well as the mass flux all increase during the periodic 'on' cycle prior to ignition, at the moment there is a small luminous sustained flame, followed by flame spreading. For the surface temperature, the fluctuation magnitude increases with increasing cycle time proportional to root tau. The in-depth temperature decay relating to the distance and cycle as proportional to exp(-x/root tau). The surface and in-depth temperatures, mass flux oscillates due to the periodic on-off irradiation with a time delay, which increases with increasing cycle and in-depth distance as proportional to root tau x. The cycle has slight influence upon the surface temperature and mass flux at the moment of ignition, where the ignition temperature maintains at about 340 degrees C, while the critical mass flux is in a range of 1-1.4 g/m(2)s, which are both independent of the external heat flux. The linear relationship of successive peak surface temperature with heat flux via time (T-5*-T-0/q ''(e))(2) proportional to t in the periodic on-off heating is retained. The theoretical predictions of the periodic ignition times derived in this study are in good agreement with the experimental measurements. Finally, compared with constant heat flux, the periodic heating delays the ignition, but with increasing cycle time, the ignition time is seen to decrease, which is primarily attributed to increases in the time-averaged irradiative heat flux. The classical model over-predicts the ignition time, the prediction error is expected to increase for long time ignition with low thermal inertia, big perturbation heat flux and long cycle time. (C) 2018 The Combustion Institute. Published by Elsevier Inc. All rights reserved.