Fabric moves along running direction continuously in the processing of weaving,dyeing and finishing and its dynamic behavior is very complex.Running at a high speed,the fabric vibrates,which has great influence not only on the performance of machine,but also on the fabric itself.Analysis of transverse free vibration of a longitudinally moving fabric is put forward in this paper and the calculating formula of natural frequencies of the fabric is introduced accordingly.Meanwhile the effects of several parameters on the first order natural frequency are also discussed.