Peer-to-Peer (P2P) streaming systems provide a large number of channels to users. The streaming capacity for a channel is defined as the maximum streaming rate that can be received by every user in the channel. In the this paper, we study the streaming capacity problem in both tree-based and mesh-based P2P live streaming systems. In tree-based multi-channel P2P live streaming systems, we propose a cross-channel resource sharing approach to improve the streaming capacity. We employ cross-channel helpers to establish the cross-channel overlay links, with which the unused upload bandwidths in a channel can be utilized to help the bandwidth-deficient peers in another channel, thus improving the streaming capacity. In meshed-based P2P live streaming systems, we formulate the streaming capacity problem into a resource optimization problem. By solving the resource optimization problem, we can optimally allocate the link rates for each peer to improve the streaming capacity. Through simulations, we demonstrate that the proposed resource sharing approaches can significantly improve the streaming capacity compared to the scheme without resource sharing.