Differential and integral muon cross-sections are calculated in water, standard rock, iron and lead, with and without the LPM effect. The corresponding cross-sections are also calculated with the dielectric suppression effect (Ter-Mikayelyan effect), in addition to the LPM effect. In our calculations the LPM effect for muons is significant from 1014 eV to 1022 eV, depending on the material, for bremsstrahlung, while it is completely negligible in the direct pair production process up to 1022 eV even for lead. The dielectric suppression effect is only important between 1012 eV and 1020 eV in the case with the LPM effect, while it is significant above 1012 eV in the case without the LPM effect.