Stimulated Raman scattering of picosecond pulses was investigated in KGd(WO4)2, and BaWO4 tungstate crystals. BaWO4 crystal was previously found to be a new very efficient material for pumping with nanosecond pulses. In our experiment, we used the second harmonic output of a mode-locked Nd:YAG laser system, which generated single pulses of 28 ps duration. The length of the crystal was 40 mm for KGW, 23 mm for KYW and 29 mm for BaWO4. The SRS threshold, conversion efficiency, and time dependence of the first Stokes with picosecond resolution were measured. Picosecond Raman gains at a 532 nm wavelength were found to be correspondingly 11.5, 18.7, and 14.4 cm/GW for KGW, KYW, and BaWO4. The Raman shifting up to the third Stokes component was detected, and the first Stokes conversion efficiency reached 30 percent in BaWO4 and 18 percent in KGd(WO4)2. Measurements of a temporal pulse length have shown that the first Stokes pulse was twice shorter than the pump pulse. The new BaWO4 crystal occurs to be an efficient solid state Raman material for a wide variety of pump pulse durations.