The rate of energy loss of muons is examined by com paring the observed depth-intensity relation with that predicted from a knowledge of the sea-level energy spectrum of cosmic ray muons. The evidence for each of the parameters entering into the analysis is assessed and estimates are made of the sea-level muon spectrum up to 10000 GeV and the depth-intensity relation down to 7000 m.w.e. The effect of range-straggling on the underground intensities is considered and shown to be important at depths below 1000 m.w.e. Following previous workers the energy loss relation is written as -dE/dx=1.88+0.077 in E'm/mc2+bE MeV g-1 cm2, where E'm is the maximum transferrable energy in a /i-e collision and m is the muon mass. The first two terms give the contribution from ionization (and excitation) loss and the third term is the combined contribution from pair production, bremsstrahlung and nuclear interaction. The best estimate of the coefficient b from the present work is b = (3.95 + 0.25) x 10-6 g-1 cm2 over the energy range 500 to 10000 GeV, which is close to the theoretical value of 4.0 x 10-6 g-1 cm2. It is concluded that there is no evidence for any marked anomaly in the energy loss processes for muons of energies up to 10000 GeV.