The influence of epitaxial strain on uniaxial magnetic anisotropy of Co 2 FeSi (CFS) and Co 2 MnSi (CMS) Heusler alloy thin films grown on (001) SrTiO 3 (STO) and MgO is reported. The in-plane biaxial strain is susceptible to tune by varying the thickness of the films on STO, while on MgO the films show in-plane easy axis for magnetization ( − → M ) irrespective of their thickness. A variational analysis of magnetic free energy functional within the Stoner-Wohlfarth coherent rotation model with out-of-plane uniaxial anisotropy for the films on STO showed the presence of magnetoelastic anisotropy with magnetostriction constant ≈ (12.22±0.07)×10 −6 and (2.02±0.06)×10 −6 , in addition to intrinsic magnetocrystalline anisotropy ≈ -1.72×10 6 erg/cm 3 and -3.94×10 6 erg/cm 3 for CFS and CMS, respectively. The single-domain phase diagram reveals a gradual transition from in-plane to out-of-plane orientation of magnetization with the decreasing film thickness. A maximum canting angle of 41.5 • with respect to film plane is predicted for the magnetization of the thinnest (12 nm) CFS film on STO. The distinct behaviour of − → M in the films with lower thickness on STO is attributed to strain-induced tetragonal distortion.