Sobol sensitivity indices assess how the output of a given mathematical model is sensitive to its inputs. If the model is stochastic then it cannot be represented as a function of the inputs , thus raising questions as how to do a sensitivity analysis in such models. Practitioners have been using a method that exploits the availability of softwares for deterministic models. For each input, the stochastic model is repeated and the outputs averaged. These averages are seen as if they were the outputs of a deterministic model and as such can feed standard softwares. In the context of limited computational resources, one must ensure that the number of repetitions of the stochastic model multiplied by the number of explorations of the input space is less than a fixed threshold. The problem of finding an optimal tradeoff between the repetitions and the explorations is addressed and the sensitivity indices corresponding to the above method are formally defined. A bound on an error criterion that penalizes bad rankings of the inputs is minimized. Moreover, exploiting a representation of stochastic models obtained from minimal distributional assumptions, another kind of Sobol-like sensitivity index is considered. Estimators of both kinds are constructed and their asymptotic properties studied. The theory is illustrated on numerical experiments.