The rest-mass effects of the muon's neutrino are discussed. The influence on the two processes-the radiative decay of π mesons and the muon-electron annihilation-in which these effects are exhibited appreciably is analysed in detail. It is shown that no conflict with existing experimental data would arise from assuming the muonic neutrino to possess a finite, not too small rest-mass. Observations for a more accurate evalution of the rest-mass of the muonic neutrino are also suggested.