In the present work, we define material functions at yielding in a perspective where elasticity and thixotropy can play an important role. These complex materials need to be characterized with a broader approach than the simple single value of the shear yield stress in a viscometric condition. Special emphasis is given to the distinction between static and dynamic yield stresses along with the distinction of viscometric and extensional yielding. The definition of static properties has no parallel with the usual material functions in nonyielding systems, like polymeric liquids, for example, where the words viscometric and extensional have a clear kinematic representation. Instead, static properties have to be measured by means of a stress state, since different stress states can be achieved where no motion takes place. We introduce the definition of material functions at yielding by specifying the yield stress tensor, an entity recently introduced by Thompson et al. [J. Nonnewton. Fluid Mech. 261, 211-219 (2018)], relative to a particular state. In this regard, we define the material functions at yielding as the components of the static and dynamic yield stress tensors in viscometric, in uniaxial extension, in biaxial extension, and in planar extension conditions. (c) 2020 The Society of Rheology.