Rate constants for vibrational relaxation of SO(B(3)Sigma(-), v' = 1 and 2) by collisions with He have been determined. SO(X(3)Sigma(-)) was generated in the photolysis of SO2 at 193 nm, and excited to a single vibrational level of the B(3)Sigma(-) state with a tunable UV laser. Dispersed fluorescence spectra were recorded as a function of buffer gas pressures (He, 30-150 Torr). Observed spectra are composed of fluorescence from the initially excited level and those from levels populated by vibrational relaxation. Kinetic analyses of relative fluorescence intensities give rate constants for both single- and double- quantum vibrational relaxation: (7.7 +/- 1.0) x 10(-13) for v' = 1 --> v' = 0,(1.0 +/- 0.2) x 10(-11) for v' = 2 --> v' = 1, and (1.7 +/- 0.3) x 10(-12) for v' = 2 --> v' = 0 ,in units of cm(3) molecule(-1) s(-1) (the quoted errors are 2sigma). It has been found that the branching ratios between quenching and vibrational relaxation of SO(A(3)Pi and B(3)Sigma(-)) by monatomic gases are strongly dependent on the number of perturbed rotational levels.