The MATHUSLA experiment is designed to investigate the possible
existence of particle dark matter in the form of Long-Lived Particles
(LLPs) produced in proton-proton collisions at the CERN High-Luminosity
Large Hadron Collider (HL-LHC). Since the MATHUSLA detector will cover a
wide area of the order of $10^{4}$ m$^2$, with 9 layers of
scintillating-detector planes, it can be used for cosmic-ray studies as
well by extending its original set-up with the insertion of a
full-coverage layer of Resistive Plate Chambers (RPCs). This will result
in a crucial improvement in detecting extensive air showers produced by
primary cosmic rays and reconstructing the arrival directions, and will
allow detailed studies of parallel-muon bundles. The detection of
hadronic showers, and the resulting study of the energy spectrum and
composition of cosmic rays, will allow a test of hadronic-interaction
models and will extended the investigation of the origin and propagation of
primary cosmic rays. In this work, an outline of the MATHUSLA experiment and its
potentialities in cosmic-ray studies are presented.