In many practical situations, to get the desired estimate or prediction, we need to process existing data. This data usually comes from measurements, and measurements are never 100% accurate. Because we only know the input values with uncertainty, the results of processing this data also comes with uncertainty. To make an appropriate decision, we need to know how accurate is the resulting estimate, i.e., how the input uncertainty "propagates" through the data processing algorithm. In the ideal case, when we know the probability distribution of each measurement error, we can, in principle, use Monte-Carlo simulations to describe the uncertainty of the data processing result. In practice, however, we often only have partial information about the measurement uncertainty: for example, instead of the exact values of the cumulative distribution function F(x), we only know bounds on F(x). Such information is known as the probability box (p-box, for short). In this paper, we provide feasible algorithms for propagating p-box uncertainty.