Measurements of strain rate sensitivity (SRS) provide a key link between dislocation-based interpretations of plastic deformation and macroscopic measurements made in mechanical tests. It is well known that plastic deformation of hexagonal close-packed (hcp) metals is achieved not only by dislocation glide but also by twinning and that the atomic rearrangement underlying the latter mode is different from that of slip. This leads to an expectation that co-activation of twinning may affect SRS of hcp metals. This assumption was tested in the present work where strain rate jump tests in both tension and compression were conducted on highly textured AZ31 plate. It was found that the SRS of the alloy in tension decreased with strain whereas that in compression increased with strain, exhibiting negative values at low strain and positive values at higher strain. Microstructure analyses revealed that the strain regimes where negative SRS or decreasing trend in SRS with strain was observed correspond to extensive twinning, implying a negative SRS of twinning. It is concluded that dislocation model alone cannot explain the strain rate dependence of flow stress in metals whose deformation is assisted by twinning.