Message passing programs commonly use buffers to avoid unnecessary synchronizations and to improve performance by overlapping communication with computation. Unfortunately, using buffers makes the program no longer portable, potentially unable to complete on systems without a sufficient number of buffers. Effective buffer use entails that the minimum number needed for a safe execution be allocated. We explore a variety of problems related to buffer allocation for safe and efficient execution of message passing programs. We show that determining the minimum number of buffers or verifying a buffer assignment are intractable problems. However, we give a polynomial time algorithm to determine the minimum number of buffers needed to allow for asynchronous execution. We extend these results to several different buffering schemes, which in some cases make the problems tractable.