It is shown that the power‐like dependence of the mean dislocation velocity v̄ on load of v̄ ∼ ϱ H0/kT type can be obtained analytically via considering the dislocation motion through a two‐dimensional random array of point obstacles. This results from stochastic averaging over the motion parameters, even in the case when the load dependence for the probability of surmounting every distinct local obstacle is described by the usual exponential relation. The v̄ ∼ ϱ H0/kT relation and its stochastic interpretation are shown to account for the number of peculiarities in stress relaxation for copper in the temperature range 4.2 to 300 K.