The purely viscoplastic paradigm has forged the understanding of yield stress materials, leading to misconceptions associated to the set of quantities that are needed to characterize yielding transition and also to the significance of the measured quantities (Thompson et al., 2018). The following assertions, usually taken for granted, are actually simplistic constitutive assumptions: (i) there exists a scalar that represents the yielding condition, (ii) there is a universal rule that maps the yield stress tensor onto that scalar, (iii) the von Mises yielding criterion holds (Thompson et al., 2018). That is, these statements are not necessarily true for a general yield stress material. In the present study we investigate the yielding of seven materials in two extensional loading conditions: traction and compression. We show that the von Mises criterion does not perform well for the yielding of these materials. A new criterion that includes the third invariant of the (deviatoric) yield stress tensor is proposed to handle the differences between traction and compression values of the stress at the yielding point. Even this criterion is not able to accommodate the yielding obtained in shear loading for these materials. In this regard, the most likely scenario is that no universal criterion exists for all kinds of yield stress materials.