Hydrogen abstraction reactions of methyl radicals or hydroxyl radicals with hydrogen sulfide are studied over the temperature range of 200-3000 K from a theoretical point of view. Potential energy surfaces are explored at the MP2/6-311++G(d,p) level. Values of 17.5 and 4.2 kJ mol(-1) were found for the barrier height of reaction CH3 + H2S at the MP4 = full/6-311++G(3df,3pd) level and of reaction OH + H2S at the QCISD = full/aug-cc-pvtz level, respectively. Rate constants of the two reactions are calculated according to generalized transition-state theory and also canonical variational transition-state theory (CVTST). According to generalized transition-state theory, both reactions showed non-Arrhenius behavior at lower and higher temperatures. The tunneling factors for both reactions are calculated at different temperatures. Characteristic tunneling temperature for reactions CH3 + H2S and OH + H2S were found to equal 277 and 340 K, respectively. The. full width of the barrier at half its height (Deltas(1/2)) were found to equal 0.37 and 0.14 Angstrom for reaction of hydrogen sulfide with CH3 or OH, respectively. According to CVTST, we have found the Arrhenius parameters for the reaction of CH3 + H2S, k(1) = 6.8 x 10(4) T-1.2 exp(-6.0 kJ mol(-1)/(RT)) L mol(-1) s(-1), and for the reaction of OH + H2S, k(2) = 9.7 x 10(9) exp(-4.5 kJ mol(-1)/(RT)) L mol(-1) s(-1).