The concept of confinement is that if energy deposition into a system occurs during durations shorter than a confinement time, the response of the system depends only on the total energy deposited and not on the deposition time. For stress confinement, the relevant response is the pressure that is produced. We have shown previously that for laser absorption by a spherical absorber, stress confinement is not valid at the core of the absorber and the tensile stresses continue to grow as the pulse duration shrinks well below any characteristic response time of the system. We have now calculated the pressure response in the cellular medium outside the absorber. We find that for a variety of energies, stress confinement is valid. We find that the characteristic confinement time agrees well with that expected for pressure transmission across the absorber. We show that even though the peak pressure that is produced varies slowly as a function of pulse duration, there is a sudden onset of shock wave production when the pulse duration is shortened below the confinement time. Since damage results from pressure gradients, the sudden onset of shock waves implies a sharp increase in the potential for damage.