Abstract: A single crystalline thermo visco-plastic constitutive model associated with an iterative algorithm was introduced.They can be used to describe the stress-strain relationship of a single crystal in an anisothermal process,and also to describe the crystalline creep and damage of a single crystal under slipping mechanism.This model and algorithm were applied to the analyses of anisothermal visco-plastic creep and damage of an air-cooled directional solidification turbine blade taking into consideration of the column crystalline grain structure.The analysis show that under the condition considered in the present paper,the air cooled directional solidification turbine blade is under going a relatively low stress,and the induced blade tip creep elongation is not more than 0.06 mm in 500 working hours.