A variational transition-state theory calculation for the reaction of OH radical with dimethyl sulfide (DMS) in the absence of oxygen is presented. The potential energy surface was previously studied and the effects of different levels of theory were analyzed. Here we propose a kinetic model for the atmospheric DMS oxidation in the absence of oxygen. For the first time, addition of OH to DMS and CH(3)SOH elimination channels are connected, and the equilibrium approximation in the high-pressure regime is applied to the DMS-OH adduct in the absence of oxygen. Both low- and high-pressure limits are considered to analyze the two different mechanisms of the H-abstraction channel, and two different kinetic approaches are applied to study them. The rate constants for the addition-elimination and H-abstraction routes are compared and the branching ratios are also studied. Tunneling contributions and kinetic isotope effects are analyzed. We conclude, in agreement with experimental observations, that in the absence of oxygen DMS oxidation takes place via H-abstraction with a branching ratio of 1.0 at atmospheric temperatures.