We show that part of the reflectance difference resonance near the E-0 energy of ZnSe is due to the anisotropic in-plane strain in the ZnSe thin films, as films grown on three distinctly different substrates, GaAs, GaP, and ZnS, all show the resonance at the same energy. Such anisotropic strain induced resonance is predicted and also observed near the E-1/E-1+Delta(1) energies in ZnSe grown on GaAs. The theory also predicts that there should be no resonance due to strain at, the E-0+Delta(0) energy, which is consistent with experiments. The strain anisotropy is rather independent of the ZnSe layer thickness, or whether the film is strain relaxed. For ZnSe films with large lattice mismatch with substrates, the resonance at the E-1/E-1+Delta(1) energies is absent, very likely due to the poor crystalline quality of the 20 nm or so surface layer.