The analysis of Rayleigh wave propagation in crystals is carried out in the cases for which, on the one hand, Christoffel equations split into two parts providing a Rayleigh wave polarized in the sagittal plane, and on the other hand, boundary conditions simplify under the conditions that some elastic constants vanish. It is shown that these requirements are satisfied by 16 configurations in crystals belonging to the orthorhombic, tetragonal, cubic, and hexagonal symmetry systems. The three particular cases solved by Stoneley [R. Stoneley, Proc. R. Soc. London, Ser. A232, 447–458 (1955)] are included. The equations giving the velocity and the mechanical displacement are established. The influence of the anisotropy factor on the decay constant is emphasized for crystals belonging to the cubic or tetragonal systems. Curves showing the decrease of the longitudinal and transverse components of the mechanical displacement are given for YAG, Si, GaAs, TiO2, and TeO2. Oscillations and a very slow decrease versus depth of the mechanical displacement components were observed for TeO2. These are ascribed to the strong anisotropy of this crystal.