Generation of robust trajectories for legged robots remains a challenging task due to the underlying nonlinear, hybrid and intrin- sically unstable dynamics which needs to be stabilized through limited contact forces. Furthermore, disturbances arising from unmodelled con- tact interactions with the environment and model mismatches can hinder the quality of the planned trajectories leading to unsafe motions. In this work, we propose to use stochastic trajectory optimization for gener- ating robust centroidal momentum trajectories to account for additive uncertainties on the model dynamics and parametric uncertainties on contact locations. Through an alternation between the robust centroidal and whole-body trajectory optimizations, we generate robust momen- tum trajectories while being consistent with the whole-body dynamics. We perform an extensive set of simulations subject to different uncer- tainties on a quadruped robot showing that our stochastic trajectory optimization problem reduces the amount of foot slippage for different gaits while achieving better performance over deterministic planning.