This research focuses on the Solid Transportation Problem characterized by multiple objectives and stochastic parameters with mixed constraints. MSSTPMC (Multi-objective Stochastic Solid Transportation Problem with Mixed Constraints) is a complex logistic optimization challenge arising in various real-world scenarios. This research aims to optimize the time and cost of transportation under probabilistic mixed constraints follows Weibull distribution. MSSTPMC is formulated as a chance constraint programming problem and includes probabilistic constraints to ensure the fulfilment of the Supply, Demand, and Conveyance capacity with specified probabilities. To optimize Multi-objective Optimization Problems, use the Fuzzy Programming Technique and the Global Criteria Method. The effectiveness of the suggested models and techniques for the MSSTPMC under uncertainty is shown by computational results.