The elastic properties and plane acoustic velocity of double perovskite Sr2CaMoO6 and Sr2CaWO6 are investigated with the plane wave pseuedopotential method based on the first-principles density functional theory within the local density approximate (LDA) and the generalized gradient approximation (GGA). The calculations indicate that Sr2CaMoO6 and Sr2CaWO6 respectively have the the Mo-O and W-O stable octahedral structure. The bulk modulus B, shear modulus G, Young’s modulus E, Poisson’s ratio ν and Debye temperature were calculated based on the elastic constants. The three dimensional plane acoustic velocities and their projection are in calculated for each direction by solving the Christoffel’s equation systematically based on the theory of acoustic waves in anisotropic solids, the result shows of anisotropy of lattice vibration for Sr2CaMoO6 is stronger than Sr2CaWO6.