In this talk we are interested in the radial solutions of semilinear wave equations with a
supercritical nonlinearity, in dimension 3, and with initial data lying in the critical Sobolev space. It is well-known that one can construct solutions on a short time interval. Then next question is: what is the asymptotic behavior of these solutions? In other words do the solutions behave like free solutions or is there blow-up? In the latter case, the standard blow-up criterion says that a Strichartz-type norm must explode. In this talk we upgrade the standard blow-up criterion. We prove that if there is blow-up, then the critical Sobolev norm must also explode.