Concurrency libraries can facilitate the development of multithreaded programs by providing concurrent implementations of familiar data types such as queues or sets. There exist many optimized algorithms that can achieve superior performance on multiprocessors by allowing concurrent data accesses without using locks. Unfortunately, such algorithms can harbor subtle concurrency bugs. Moreover, they require memory ordering fences to function correctly on relaxed memory models. To address these difficulties, we propose a verification approach that can exhaustively check all concurrent executions of a given test program on a relaxed memory model and can verify that they are observationally equivalent to a sequential execution. Our Check- Fence prototype automatically translates the C implementation code and the test program into a SAT formula, hands the latter to a standard SAT solver, and constructs counterexample traces if there exist incorrect executions. Applying CheckFence to five previously published algorithms, we were able to (1) find several bugs (some not previously known), and (2) determine how to place memory ordering fences for relaxed memory models.