  We consider the massive integer higher spin fields coupled to an external
constant electromagnetic field in flat space of arbitrary dimension and find a
gauge invariant quartic interaction vertex which is quadratic in dynamical
higher spin field and quadratic in external field. Construction of the vertex
is based on the BRST approach to higher spin filed theory where no off-shell
constraints on the fields and on the gauge parameters are imposed from the very
beginning (unconstrained formulation).
