  We use the stability conditions of the Landau parameters for the symmetric
nuclear matter and pure neutron matter to calculate the critical densities for
the Skyrme type effective nucleon-nucleon interactions. We find that the
critical density can be maximized by adjusting appropriately the values of the
enhancement factor $\kappa$ associated with isovector giant dipole resonance,
the quantity $L$ which is directly related to the slope of the symmetry energy
and the Landau parameter $G_0^\prime$. However, restricting $\kappa$, $L$ and
$G_0^\prime$ to vary within acceptable limits reduces the maximum value for the
critical density $\tilde\rho_{cr}$ by $\sim 25%$. We also show that among the
various quantities characterizing the symmetric nuclear matter,
$\tilde\rho_{cr}$ depends strongly on the isoscalar effective mass $m^*/m$ and
surface energy coefficient $E_s$. For realistic values of $m^*/m$ and $E_s$ we
get $\tilde\rho_{cr} = 2\rho_0$ to $ 3\rho_0$ ($\rho_0 = 0.16$fm$^{-3}$).
