  We establish growth tightness for a class of groups acting geometrically on a
geodesic metric space and containing a contracting element. As a consequence,
any group with nontrivial Floyd boundary are proven to be growth tight with
respect to word metrics. In particular, all non-elementary relatively
hyperbolic group are growth tight. This generalizes previous works of
Arzhantseva-Lysenok and Sambusetti. Another interesting consequence is that
CAT(0) groups with rank-1 elements are growth tight with respect to
CAT(0)-metric.
