Abstract: According to the elastic yarn pulling test stress and the strain curve characteristic,an elastic yarn stress and strain mathematical model was established using index fitting method,Correlation coefficientRof the model indicated that the obtained relationship is reliable.Then based on elastic yarn physical structure,a stress and strain physical model has been developed theoretically.The stress-strain curve obtained by this model is similar to that by the mathematical model.On this basis the tow quality parameters describing elastic yarn quality parameters are defined,and experimental results reveal that the elastic yarn quality obtained by the quality parameter evaluation is in good agreement with the actual yarn quality,showing certain application value in practice.