Apparent elongational yield stresses of soft matter including polymer gels, highly concentrated emulsions, and aggregated suspensions have been determined from step stretch experiments. Materials display apparent shear yield stresses in the range 1-100 Pa and large but finite shear relaxation times t(R). For all investigated fluids, the Laplace pressure within the stretched filaments is essentially constant during an initial period of time after the step strain. Then, it increases rapidly and finally the filaments break. Filament lifetime t(f) strongly increases with decreasing stretching ratio e. The apparent elongational yield stress is identified as the initial value of the Laplace pressure obtained at a critical stretching ratio epsilon(c) corresponding to a Deborah number De = t(R)/t(f) = 1. For all fluids, the ratio of this elongational yield stress to shear yield stress is root 3 in agreement with the von Mises plasticity criterion, irrespective of the physical nature of structural breakdown. Elongational experiments performed at different epsilon or t(f) covering Deborah numbers between 0.1 and 100 reveal a universal relationship between the initial plateau value of the Laplace pressure normalized to the shear yield stress and De. This stress ratio varies between 0.5 and 5, and equals root 3 only for De approximate to 1. (C) 2013 The Society of Rheology. [http://dx.doi.org/10.1122/1.4789785]