We study compactifications of string theory and M-theory to six dimensions with background fluxes. The non-zero fluxes lead to additional mass parameters. We derive the S- and T-duality rules for the corresponding (massive) supergravity theories. Specifically, we investigate the massive T-duality between Type IIA superstring theory compactified on K3 with background fluxes and Type IIB superstring theory compactified on K3. Furthermore, we generalize to the massive case the 6D 'string–string' S-duality between M-theory on K3 × S¹ and the heterotic string on T⁴. Whereas in the case of massive T-duality the mass parameters are in the fundamental representation of the U-duality group O(4, 20) we find that in the case of massive S-duality they are in the 3-index antisymmetric representation. In the latter case, the mass parameters involved extend those of Kaloper and Myers. We apply our duality rules to massive brane solutions, such as the domain wall solutions corresponding to the mass parameters and find new massive brane solutions. Finally, we discuss the higher dimensional interpretation of the dualities and brane solutions.