Dynamic processes of deformation in tensile experiments of plates of SUS304 stainless steels at low strain rates less than 10-4 s-1 were investigated by dynamic ESPI (DESPI). Full-field deformation behaviors could be observed continuously and totally as moving speckle correlation patterns from the start of a tensile test to fracture of a specimen. In later stage of plastic deformation, anomalous stress fluctuations or projections in a stress-strain curve were found. Correspondingly, characteristic X-shaped strain localizations which swept over the specimen repeatedly were found. Dependence of anomalous deformation behavior on strain rate was precisely examined. Changes in magnetic properties before and after passing the X-shaped strain localization were also investigated by the ferritescope. Propagating strain localization can be considered as the front of strain induced martensitic transformation.