  Binary population synthesis shows that mass transfer from a giant star to a
main-sequence (MS) companion may account for some observed long-orbital period
blue stragglers. However, little attention {\bf is paid to this blue straggler
formation scenario} as dynamical instability often happens when the mass donor
is a giant star. In this paper, we have studied the critical mass ratio,
$q_{\rm c}$, for dynamically stable mass transfer from a giant star to a MS
companion using detailed evolution calculations. The results show that a more
evolved star is generally less stable for Roche lobe overflow. Meanwhile,
$q_{\rm c}$ almost linearly increases with the amount of the mass and angular
momentum {\bf lost} during mass transfer, but has little dependance on stellar
wind. To conveniently use the result, we give a fit of $q_{\rm c}$ as a
function of the stellar radius at the onset of Roche lobe overflow and of the
mass transfer efficiency during the Roche lobe overflow.
  To examine the formation of blue stragglers from mass transfer between giants
and MS stars, we have performed Monte Carlo simulations with various $q_{\rm
c}$. {\bf The simulations show that some binaries with the mass donor on the
first giant branch may contribute to blue stragglers with $q_{\rm c}$ obtained
in this paper but will not from previous $q_{\rm c}$. Meanwhile, from our
$q_{\rm c}$, blue stragglers from the mass transfer between an AGB star and a
MS companion may be more numerous and have a wider range of orbital periods
than those from the other $q_{\rm c}$.
