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This paper contributes to the development of techniques for the modular proof of programs that include concurrent algorithms. We present a proof of a non-blocking concurrent algorithm, which provides a shared stack. The inter-thread interference, which is essential to the algorithm, is confined in the proof and the specification to the modular operations, which perform push and pop on the stack. This is achieved by the mechanisms of separation logic. The effect is that inter-thread interference does not pollute specification or verification of clients of the stack.