  We analyze an analog of the hydrodynamic Rayleigh-Taylor instability for the
liquid-solid phase interface under non-uniform growth of the solid phase. The
development of the instability starts on conditions of an accelerated interface
growth and if the magnitude of acceleration exceeds some critical value. The
plane and spherical shapes of the interface are considered. The observation of
the instability can be expected for helium crystals in the course of their
abnormal fast growth.
