Using a well-entangled monodisperse styrene-butadiene random-copolymer (SBR) melt as a model system, we illustrate generic features of uniaxial extension behavior that may be shared by all well-entangled thermoplastic and elastomeric materials. Depending on the imposed extensional rate, the same sample may behave like a viscous liquid or an elastic “solid.” Analogous to the recently revealed shear inhomogeneity, the SBR melt inevitably undergoes cohesive failure in the form of sample breakage whenever the Weissenberg number is much greater than unity, making it challenging to reach steady state. In the elastic deformation regime where the external deformation rate is faster than Rouse relaxation rate, the sample undergoes a finite amount of uniform stretching before yielding occurs in a period much shorter than the terminal relaxation time. Steady flow can be achieved only in the terminal regime where entangled chains utilize directed molecular diffusion to achieve rearrangement and enable uniform flow.