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Network coding allows a network node to code the information flows before forwarding them. While it has been theoretically proved that network coding can achieve maximum network throughput, the theoretical results usually do not consider the burstiness of data traffic, delays, and the stochastic nature in information processing and transmission. There is currently no theory to systematically model and evaluate the performance of network coding, especially when node's capacity (i.e., coding and transmission) becomes stochastic. Without such a theory, the performance of network coding under various system settings is far from clear. To fill the vacancy, we develop an analytical approach by extending the stochastic network calculus theory to tackle the special difficulties in the evaluation of network coding. We prove the new properties of the stochastic network calculus and design an algorithm to obtain the performance bounds for acyclic stochastic networks with network coding. The tightness of theoretical bounds is validated with simulation.