  We consider the effect of electron-phonon coupling in semimetals in high
magnetic fields, with regard to elastic modes that can lead to a redistribution
of carriers between pockets. We show that in a clean three dimensional system,
at each Landau level crossing, this leads to a discontinuity in the
magnetostriction, and a divergent contribution to the elastic modulus. We
estimate the magnitude of this effect in the group V semimetal Bismuth.
