A time-dependent analytical thermal model of the temperature and the corresponding induced thermal stresses on the pump face of quasi continuous wave (qcw) end-pumped laser rods is derived. We apply the model to qcw diode-end-pumped rods and show the maximum peak pump power that can be utilized without fracturing the rod. To illustrate an application of the model, it is applied to a qcw pumped Tm: YLF rod and found to be in very good agreement with published experimental results. The results indicate new criteria to avoid fracture when operating Tm: YLF rods at low qcw pump duty cycles.(C) 2008 Optical Society of America.