We investigate the pressure-induced superfluid-solid transition of He4 at T=0. Neglecting the accidental instability against nucleation, we find a definite stability limit at which the superfluid phase becomes intrinsically unstable against a density fluctuation number QL. We find that the roton minimum with frequency ω(QL) is the soft mode associated with this stability limit. This interpretation reflects the observed pressure dependence both of the roton minimum and of the first maximum of the structure factor at QL. © 1971 The American Physical Society.