Interval computations usually deal with the case of epistemic uncertainty, when the only information that we have about a value of a quantity is that this value is contained in a given interval. However, intervals can also represent aleatory uncertainty -- when we know that each value from this interval is actually attained for some object at some moment of time. In this paper, we analyze how to take such aleatory uncertainty into account when processing data. We show that in case when different quantities are independent, we can use the same formulas for dealing with aleatory uncertainty as we use for epistemic one. We also provide formulas for processing aleatory intervals in situations when we have no information about the dependence between the inputs quantities.