Muon beam-induced plasma loading of radio-frequency (RF) cavities filled with high pressure hydrogen gas with 1% dry air dopant has been studied via numerical simulations. The electromagnetic code SPACE, that resolves relevant atomic physics processes, including ionization by the muon beam, electron attachment to dopant molecules, and electron-ion and ion-ion recombination, has been used. Simulations studies have been performed in the range of parameters typical for practical muon cooling channels.