In this paper, we considered a multi-objective stochastic transportation problem where the supply and demand parameters follow extreme value distribution having three-parameters. The proposed mathematical model for stochastic transportation problem cannot be solved directly by mathematical approaches. Therefore, we converted it to an equivalent deterministic multi-objective mathematical programming problem. For solving the deterministic multi-objective mathematical programming problem, we used an $\epsilon$-constraint method. A case study is provided to illustrate the methodology.