This paper addresses the Multi-Objective Stochastic Traveling Salesman Problem (MO-STSP), where travel distances and times are modeled as stochastic variables following a uniform distribution. To manage the inherent uncertainty, the problem is first transformed into a deterministic form using the expected values of these stochastic parameters. Subsequently, heuristic methods are applied to solve the deterministic version. Specifically, two approaches are proposed: the 2-Opt local search algorithm, which iteratively refines local solutions through edge rearrangement, and Monte Carlo simulations, which explore the solution space via random sampling. Both methods were selected for their effectiveness in managing the complexities and uncertainties associated with the MO-STSP. Implemented in Python and tested on random instances, these methods provide robust solutions that balance travel distance and time. The study includes a comparative analysis of the two heuristics, highlighting their strengths and trade-offs, and suggests practical applications in logistics and transportation. This research contributes to the field of stochastic optimization by demonstrating the effectiveness of using expected values and heuristic techniques to address the MO-STSP and proposes future research directions, including the integration of advanced metaheuristics.