  The crust region is a tiny fraction of neutron stars, but it has a variety of
physical properties and plays an important role in astronomical observations.
One of the properties characterizing the crust is the elasticity. In this
review, with the approach of asteroseismology, we systematically examine
neutron star oscillations excited by crust elasticity, adopting the Cowling
approximation. In particular, by identifying the quasi-periodic oscillations
observed in magnetar flares with the torsional oscillations, we make a
constraint on the nuclear saturation parameters. In addition, we also discuss
how the shear and interface modes depend on the neutron star properties. Once
one detects an additional signal associated with neutron star oscillations, one
can get a more severe constraint on the saturation parameters and/or neutron
star properties, which must be a qualitatively different constraint obtained
from terrestrial experiments, and help us to complementarily understand
astrophysics and nuclear physics.
