Currently the most advanced and mature plasma facing unit (PFU) technology is the ITER W/Cu PFU, which is monoblock composed of tungsten, copper and CuCrZr as plasma facing material, interlayer and heat sink, respectively. Fatigue failure in heat sink structural including fracture under H-mode (High confinement mode) operating condition greatly influence the lifetime of divertor target. In this study, to simplify calculation for complex heat load input, the heat load time evolution with ELMs(Edge localized modes) was defined as an equivalent heat flux for steady-state analysis. To investigate the fatigue damage behavior of CuCrZr tube in EAST divertor monoblock, the thermal-stress analysis was performed firstly with regards to EAST operating and cooling condition. The stress and strain distribution on heat sink tube indicates that the risky position is on the upper inner surface of tube. Combined with the strain-life relationship, the fatigue life and creep-fatigue damage of CuCrZr tube was assessed. The fatigue analysis shows that the cumulative fatigue and creep damage on tube meet the requirement under operating condition now available and it is great influenced by steady heat load. The tube also risks cracking and fracture under long pulse operation in future fusion device. The stress intensity factor and J-integral were applied to investigate crack fracture in risky position on heat sink tube that the pre-crack shows no risk of fast fracture but potential for creep at higher operating temperature.