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 lev
el 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.
