In this paper, we study the fault tolerance of 3-D mesh networks under a more realistic model in which each network node has an independent failure probability. We develop a novel technique to formally derive lower bounds on the connectivity probability for 3-D mesh networks. Our study shows that 3-D mesh networks of practical size can tolerate a large number of faulty nodes thus are reliable enough for multicomputer systems. We also show a number of advantages of 3-D mesh networks over other popular network topologies. For example, compared to 2-D mesh networks, 3-D mesh networks are much stronger in tolerating faulty nodes, while for practical network size, the fault tolerance of 3-D mesh networks is comparable with that of hypercube networks but enjoys much lower node degree in the networks.