We report experimental measurements of high extensibility of several yield-stress fluids, demonstrating a behavior completely outside the standard paradigm of model materials and constitutive equations for yield-stress fluids. We identify "highly" extensible materials using uniaxial tension tests, as materials with values of strain-to-break larger than predictions from the tensorial Herschel-Bulkley model, and larger strain-to-break than some of the most studied model materials including aqueous microgel particle suspensions (Carbopol), and aqueous clay suspensions (Laponite and Bentonite). Materials in commercial use, including a printing resin, chewing gums, and food products, have a yield stress but do not rupture until reaching extremely large extensional deformations. The purpose of this work is to introduce a method for characterizing the extensibility of yield-stress fluids, demonstrate the range of extensibility seen in real yield-stress fluids (commercial products, biomaterials), and introduce one possible model material for highly extensible yield-stress fluids: Silicone oil droplets emulsified at moderate volume fraction into an aqueous solution of polyvinyl alcohol cross-linked by sodium tetraborate. (C) 2018 The Society of Rheology.