Surface acoustic wave (SAW) propogation in Y-cut and Z-cut relaxor-based 0.67Pb(Mg1/3Nb2/3)O3–0.33PbTiO3 (PMN-33%PT) ferroelectric single crystals poled along c cubic direction has been analyzed theoretically. Characteristic curves were obtained for the phase velocity, electromechanical coupling coefficient and PFA of SAW in Y-cut and Z-cut PMN-33%PT single crystals. It was found that the phase velocity is lower, while the electromechanical coupling coefficient is much higher, than that of traditional piezoelectric materials. The power flow angle (PFA) can be zero in certain directions, which makes this crystal system a promising material for future SAW devices with smaller size and enhanced performance. The directions near 45° and 135° of Y-cut PMN-33%PT crystals are found to be optimum directions for SAW device applications.