This paper merges the existing smuggling literature with the literature concerning competitive firm behavior under uncertainty. A stochastic, joint product, model of smuggling is developed. The model introduces production uncertainty, generated by enforcement activity, into a Pitt (1981) type of smuggling production function. This modelling technique allows the trade pattern and welfare results which evolve under smuggling with uncertainty to be compared to smuggling in a world of certainty. It is demonstrated that mere presence of uncertainty increases the real resource cost associated with smuggling, reduces legal and illegal trade, and welfare, when compared to smuggling in a world of certainty