A model of the photon avalanche in a four level coupled system is proposed. The general condition to generate the avalanche has been theoretically analysed. The avalanche threshold and the temporal behavior of the avalanche fluorescence intensity when the pump rate is below or above the threshold are discussed in details. Then this model in combining with the numerical approach is applied to the case of Tm³⁺:LiYF ₄ crystal. Theoretical results agree with the experiment on the whole. This model and the obtained results are helpful for developing new type avalanche upconversion materials.