The Molecular Distance Geometry Problem consists in finding the three-dimensional conformation of a protein using some of the distances between its atoms provided by experiments of Nuclear Magnetic Resonance. This is a continuous search problem that can be discretized under some assumptions on the known distances. We discuss the case where some of the distances are subject to uncertainty within a given nonnegative interval. We show that a discretization is still possible and propose an algorithm to solve the problem. Computational experiments on a set of artificially generated instances are presented.