Cosmic ray radiation, thanks to its high penetration capability and relative abundance, has been successfully used in scientific research and civil applications for a long time. For example, techniques based on the attenuation of cosmic ray muons or on their angular scattering have been used to study the inner structure of volcanoes, to search for hidden chambers in Egyptian pyramids, to inspect nuclear waste containers and to monitor blast furnaces. In addition to these imaging techniques, cosmic ray muons have also been used for the detector alignment in large experiments in nuclear and elementary particle physics. In this context, a cosmic muon detection system for the stability monitoring of historical buildings will be here presented. The employment of cosmic rays is envisaged where the time scale of deformations is typically very long, and where conservation constraints could prevent the use of standard mechanical systems. The stability monitoring of Palazzo della Loggia (Brescia, Italy) has been considered as a case study, and performance and limitations of the technique have been evaluated using Monte Carlo (MC) simulations. A muon detection system based on two telescopes with three sensitive layers of scintillating fibers coupled to silicon photomultipliers has been studied. Results from MC studies, taking into account systematic uncertainties, are here presented. Finally, the main features and performance of a small-size detector prototype, developed as a proof of principle and consisting of three layers of 3x3 mm 2 scintillating fibers, as those used in the simulations, are also described.