It has been reported widely for more than half a century period that the crack growth rate increases abruptly and significantly in spite that the input strain energy release rate is kept constant, named a velocity jump, when rate of tear fracture of cross-linked rubbers approaches the velocity of elastic wave. This phenomenon is associated closely with the balance of elasticity and viscosity of the material and hence its glass transition behavior. Recently the authors summarized and defined this unstable behavior as an elastic-viscous transition phenomenon in fracture of rubber using an elastic-viscous transition diagram, where the diagram consists of three zones, each with a different fracture mode. These are an elastic-brittle fracture zone I, a viscous-ductile fracture zone III and an intermediate transition zone II between the elastic and viscous zones characterized by unstable stick-slip motions and the corresponding velocity jump. In the first half of this article, the authors show real aspects of these phenomena in detail focusing on the fracture surface formation and the stick-slip motion in the transition zone II and in the latter half we propose a new physical aspect for this transition phenomenon accompanied with velocity jump.