In this study, comprehensive study of supply chain and it’s components have been done in order to better understand significance of supply chain network design. Then a mixed integer non-linear mathematical model is presented for designing a three level, multi-commodity and multi-site supply chain with uncertainties. The purpose of this three level model are determine number and location of distribution centers and determine suitable capacity for keeping products at these centers and assign distribution centers to demand centers and suppliers to distribution centers in order to satisfy customer products requirement, determine number and type of required traort vehicle to carry products from suppliers to distribution centers and determine order amount of products at each distribution centers so that total supply chain cost is minimized and capacity constraint at distribution centers warehouse and communication paths between supply-distribution centers and distribution-demand centers are satisfied. According to proposed mathematical model, the problem is NP-hard and to solve this problem in large scale needs too much time. So two meta-heuristic solving methods based on genetic algorithm and simulated annealing algorithm in order to solve proposed model had been used and their efficiency had been studied. In small scales for two first problem sets, obtained results from GAMS software compare with obtained results from GA and SA algorithms. Solving average time in these sets by GAMS is quite high while this amount for GA and SA is negligible. Low running average time and error amount average at these problems has been shown high proposed algorithm efficiency. In medium and large scale and two problem sets of small scales, two GA and SA approach had been used and their efficiency had been studied. The obtained results from solving different problems showed that GA just in 8 instances performs better than SA and in other instances SA obtained better or at least equal than GA. Furthermore results showed SA solving average time less than GA and SA solution quality is better than GA.