We introduce MoULDyS, that implements efficient offline and online monitoring algorithms of black-box cyber-physical systems w.r.t. safety properties. MoULDyS takes as input an uncertain log (with noisy and missing samples), as well as a bounding model in the form of an uncertain linear system; this latter model plays the role of an over-approximation so as to reduce the number of false alarms. MoULDyS is Python-based and available under the GNU General Public License v3.0 (gpl-3.0). We further provide easy-to-use scripts to recreate the results of two case studies introduced in an earlier work.