Radial stability of the continuous pressure gravastar is studied using the conventional Chandrasekhar method. The equation of state for the static gravastar solutions is derived and Einstein equations for small perturbations around the equilibrium are solved as an eigenvalue problem for radial pulsations. Within the model there exists a set of parameters leading to a stable fundamental mode, thus proving the radial stability of the continuous pressure gravastar. It is also shown that the central energy density possesses an extremum in ? sub()cR) curve which represents a splitting point between stable and unstable gravastar configurations. As such the ? sub()cR) curve for the gravastar mimics the famous M(R) curve for a polytrope. Together with the former axial stability calculations this work completes the stability problem of the continuous pressure gravastar.