  We develop a theory of the magnetostriction for metals with small
charge-carrier pockets of their Fermi surfaces. As an example, we consider LuAs
that has a cubic crystal structure. The theory quite well describes the known
experimental data on the magnetostriction of this metal. The obtained results
also clearly demonstrate that the dilatometry can be used for detecting tiny
Fermi-surface pockets that are not discerned by traditional methods based on
investigations of the Shubnikov--de Haas and de Haas--van Alphen effects.
