The complex multiphase morphology of thermoplastic elastomers based on styrene-block copolymers (TPSs) affects their flow behavior significantly and in a way which may not be considered by commonly used characterization and evaluation procedures. To evaluate the relevance of non-Newtonian flow phenomena for the validity of rheometric data in processing, three commercially available TPSs with comparable hardness of about 60 Shore A but with different application fields were selected and characterized using parallel plate and high-pressure capillary rheometry. The validity of the rheometric data is assessed by modeling the flow in a high-pressure capillary rheometer by a computational fluid dynamics (CFD) simulation. The results were discussed in conjunction with close-up images of samples taken after the measurement. The materials show clearly different rheological behaviors but depend on the respective shear and geometrical conditions. In particular, for the material with the lowest viscosity, doubling the capillary diameter resulted in a disproportionate increase of the pressure loss by up to one third. Only the capillary flow of this material could not be reproduced by the CFD simulation. The results indicate that conventionally determined rheometric data of TPSs are of limited use in evaluating process flows for various material grades.