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The lattice dynamics and elastic properties of the ternary Zn x Cd 1−x Se alloy have been studied using first-principle calculations. These are done using the density-functional perturbation theory (DFPT) within local density approximation (LDA) and employing virtual-crystal approximation (VCA). We study the variation of the optical phonon frequencies (ω TO and ω LO ), the high-frequency dielectric coefficient (ε ∞ ), the dynamic effective charge (Z * ) and the elastic constants (C 11 , C 12 , C 44 ) as a function of the composition (x). We found that the ω TO and ω LO follow a quadratic law in x and agree well with the experiment. The obtained ε ∞ , Z * , C 11 , C 12 and C 44 have a quadratic form with x. The elastic constant tensors for simple cubic eight-atom supercells with x = 0.25, 0.5 and 0.75 have been computed and are in good agreement with those obtained from VCA.