  We examine neutral-current quasi-elastic neutrino-nucleus reactions on
$^{12}$C and $^{208}$Pb targets. We use the relativistic mean field theory
approach to describe the nuclear dynamics. We compute the cross sections for
the scattering of 150-MeV, 500-MeV and 1000-MeV neutrinos on a $^{12}$C target
and study the effect of the strange-quark content of the nucleon which appears
in these reactions via the isoscalar weak current. We compare our results with
the data of the MiniBooNE experiment for mineral oil (CH$_2$). We also
calculate the cross section for the quasi-elastic neutron knockout reaction of
20 to 60-MeV neutrinos on a $^{208}$Pb target which is relevant to plans to use
lead as a target material in future supernova neutrino detectors.
