The magnetic anisotropy parameters in [110] MBE-grown films of REFe 2 (RE, rare earth) compounds are not the same as those in the bulk. This is due to the presence of a shear strain ε xy , frozen-in during crystal growth. In this paper, magnetic anisotropy parameters for [110] MBE-grown REFe 2 films, that directly involve the shear strain ε xy , are presented and discussed. In addition to the usual first-order Callen and Callen termK 2 , there are nine second-order terms, six of which involve cross-terms between ε xy and the cubic crystal field terms B 4 and B 6 . Two of the second-order cross-terms are identified as being important:K 242 (T ) andK 264 (T ). Of these, the rank-two termK 242 (T ) dominates over a large temperature range. It has the same angular dependence as the first-order termK 2 , but with a more rapid temperature dependence. The correction at T = 0 K for TbFe 2 , DyFe 2 , HoFe 2 , ErFe 2 and TmFe 2 , amounts to ∼+9.2%, −13.9%, −11.6%, +14.3%, and 27.1%, respectively. Similar comments are made concerning the rank-fourK 264 (T ) term.