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Rheological models for biobased plastics can assist in predicting optimum processing parameters in industrial forming processes for biobased plastics and their composites such as film blowing, or injection stretch-blow molding in the packaging industry. Mathematical descriptions of polymer behavior during these forming processes are challenging, as they involve highly nonlinear, time-, temperature-, and strain-dependent physical deformation processes in the material, and have not been sufficiently tested against experimental data in those regimes. Therefore, the predictive capability of two polymer models, a classical Giesekus and a physically-based Rolie-Poly, is compared here for extensional and shear rheology data obtained on a poly(L-lactide) (PLLA) across a wide range of strain rates of relevance to those forming processes. Generally, elongational and shear melt flow behavior of PLLA was predicted to a satisfactory degree by both models across a wide range of strain rates (for strain rates 0.05–10.0 s−1), within the strain window up to 1.0. Both models show a better predictive capability for smaller strain rates, and no significant differences between their predictions were found. Hence, as the Giesekus model generally needs a smaller number of parameters, this class of models is more attractive when considering their use in computationally demanding forming simulations of biobased thermoplastics. [ABSTRACT FROM AUTHOR]