The inclusion-exclusion principle is a well-known property of set and probability theories, that is instrumental to solve some problems such as the evaluation of systems reliability or of uncertainty over Boolean formulas. However, when using models that mixes sets and probabilities, this principle does not longer hold in general. It is therefore useful to know in which cases it continues to hold. This paper investigates this question when the models of uncertainty are belief functions. After exhibiting sufficient and necessary conditions for the principle to hold, we illustrate its use on some applications, i.e. reliability analysis and uncertainty over Boolean formulas.