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A dynamic system model of continuous manufacturing systems has been developed based on analogies with electrical systems. This model has the capability to model both deterministic and stochastic systems. The model provides physically meaningful governing equations to describe both the steady state and transient responses of continuous manufacturing systems. For stochastic solutions, the model is not limited to any specific probabilistic distribution. The model is demonstrated by application to a representative continuous manufacturing line for both deterministic and stochastic cases. The results of the stochastic case are compared to those from a discrete event simulation tool using a paired t-test at the 95% confidence level. For some results, the difference is statistically insignificant. For others, there is a statistically significant difference. However, in both cases the percentage difference is within a reasonable range.