  The Starobinsky model is a natural inflationary scenario in which inflation
arises due to quantum effects of the massless matter fields. A modified version
of the Starobinsky (MSt) model takes the masses of matter fields and the
cosmological constant, $\Lambda$, into account. The equations of motion become
much more complicated however approximate analytic and numeric solutions are
possible. In the MSt model, inflation starts due to the supersymmetric (SUSY)
particle content of the underlying theory and the transition to the radiation
dominated epoch occurs due to the relatively heavy s-particles decoupling. For
$\Lambda=0$ the inflationary solution is stable until the last stage, just
before decoupling. In the present paper we generalize this result for
$\Lambda\neq 0$, since $\Lambda$ should be non-vanishing at the SUSY scale. We
also take into account the radiative corrections to $\Lambda$. The main result
is that the inflationary solution of the MSt model remains robust and stable.
