The global sensitivity analysis, used to quantify the influence of uncertain input parameters on the response variability of a numerical model, is applicable to deterministic computer codes (for which the same set of input parameters gives always the same output value). This paper proposes a global sensitivity analysis method for stochastic computer codes (having a variability induced by some uncontrollable parameters). The mean and dispersion of the code outputs are modeled by two interlinked Generalized Additive Models (GAM). The "mean" model allows to obtain the controllable parameters sensitivity indices, while the "dispersion" model allows to obtain the uncontrollable parameters ones. The relevance of the proposed model is analyzed with two case studies. Results show that the joint modeling approach leads to more accurate sensitivity index estimations, especially for the joint GAM model.