Abstract. Cosmic ray radiation is mostly composed, at sea level, by high energy muons, which are highly penetrating particles capable of crossing kilometers of rock. Cosmic ray radiation constituted the first source of projectiles used to investigate the intimate structure of matter and is currently and largely used for particle detector test and calibration. The ubiquitous and steady presence at the Earth's surface and the high penetration capability has motivated the use of cosmic ray radiation also in fields beyond particle physics, from geological and archaeological studies to industrial applications and civil security. In the present paper, cosmic ray muon detection techniques are assessed for stability monitoring applications in the field of civil engineering, in particular for static monitoring of historical buildings, where conservation constraints are more severe and the time evolution of the deformation phenomena under study may be of the order of months or years. As a significant case study, the monitoring of the wooden vaulted roof of the "Palazzo della Loggia" in the town of Brescia, in Italy, has been considered. The feasibility as well as the performances and limitations of a monitoring system based on cosmic ray tracking, in the considered case, have been studied by Monte Carlo simulation and discussed in comparison with more traditional monitoring systems. Requirements for muon detectors suitable for this particular application, as well as the results of some preliminary tests on a muon detector prototype based on scintillating fibers and silicon photomultipliers SiPM are presented.