The CaRMnSnO6 (R = La, Pr, Nd, Sm-Dy) double perovskites were prepared using a solid state reaction in evacuated sealed silica tubes at 1050-1100°C. All compounds belong to the GdFeO3-type structure (orthorhombic a:b:c ≈ √2ap : 2ap : √2a p unit cell, space group Pnma, (a+b-b -) tilt system). The crystal structures were investigated by electron diffraction and high resolution electron microscopy and were refined from X-ray powder diffraction data for the R = La, Sm, Dy representatives (La: R I = 0.030, RP = 0.033; Sm: RI = 0.030, R P = 0.010; Dy: RI = 0.033, RP = 0.010). A disordered arrangement of the Ca and R cations over the A positions and Mn and Sn cations over the B positions was found in all cases. The small difference in charge and size between the Mn3+ and Sn4+ cations, the small degree of Jahn-Teller deformation of the MnO6 octahedra, and the ac-plane orbital ordering type were proposed as possible reasons for the cation disorder on the B sublattice. The compounds demonstrate a spin glass behavior in the temperature range from 25 to 300 K.