  In this paper we used the theory of adiabatic radial oscillations developed
by Chandrasekhar to study the conditions for dynamical stability of constant
energy-density stars, or Schwarzschild stars, in the unstudied ultra compact
regime beyond the Buchdahl limit, that is, for configurations with radius $R$
in the range $R_{\rm S}<R<(9/8)R_{\rm S}$, where $R_{\rm S}$ is the
Schwarzschild radius of the star. These recently found analytical solutions
exhibit a negative pressure region in their centre and, in the limit when $R\to
R_{\rm S}$, the full interior region of the star becomes filled with negative
pressure. Here we present a systematic analysis of the stability of these
configurations against radial perturbations. We found that, contrary to the
usual expectation found in many classical works, the ultra compact
Schwarzschild star is stable against radial oscillations. We computed values of
the critical adiabatic index $\gamma_{c}$ for several stellar models with
varying radius $R/R_{\rm S}$ and found that it also approaches a finite value
as $R/R_{\rm S} \to 1$
