Using rheometry in this study, we comprehensively investigated the effect of shear and extensional flow fields on the crystallization behavior of linear and branched poly(lactic-acid) (PLA). The shear-induced isothermal crystallization was explored in a stress-growth experiment during which continuous low shear rates of 0.01 and 0.1 s(-1) were applied at a given temperature. To examine the effect of strong shear flow on the crystallization of PLAs, the samples were pre-sheared at high shear rates of 1 and 10 s(-1) and subsequently isothermally crystallized at 140 degrees C. Results revealed that, at a given deformation rate, branched PLA exhibited a much faster crystallization rate than that of linear PLA. Also, altering the deformation rate at low shear rates could hardly affect the crystallization kinetics of both PLAs whereas the crystallization was strongly dependent on the shear rate value when pre-sheared at strong shear flows. The elongational flow-induced crystallization behavior of branched PLA by means of rheometry was also explored for the first time. It was shown that the elongational flow introduced a much more pronounced influence on branched PLA crystallization kinetics than that induced by the shear flows. The crystallization kinetics and structure of the sheared and stretched branched PLA samples were also investigated and confirmed using a differential scanning calorimeter (DCS), and wide- and short-angle X-ray scattering (WAXS and SAXS).