Understanding the real achievable performance of mobile ad hoc networks (MANETs) under practical network constraints is of great importance for their applications in future highly heterogeneous wireless network environments. This paper explores, for the first time, the performance modeling for MANETs under a general limited buffer constraint, where each network node maintains a limited source buffer of size $B_s$ to store its locally generated packets and also a limited shared relay buffer of size $B_r$ to store relay packets for other nodes. Based on the Queuing theory and birth-death chain theory, we first develop a general theoretical framework to fully depict the source/relay buffer occupancy process in such a MANET, which applies to any distributed MAC protocol and any mobility model that leads to the uniform distribution of nodes' locations in steady state. With the help of this framework, we then derive the exact expressions of several key network performance metrics, including achievable throughput, throughput capacity, and expected end-to-end delay. We further conduct case studies under two network scenarios and provide the corresponding theoretical/simulation results to demonstrate the application as well as the efficiency of our theoretical framework. Finally, we present extensive numerical results to illustrate the impacts of buffer constraint on the performance of a buffer-limited MANET.