The thermal motion of atoms and, in other words, thermal fluctuations or distortions of crystal lattice caused by this motion lead to a wavy shape of the dislocation line both in alloys, where there are dissolved atoms, and in pure metals, where there are no such atoms. The wavy shape of the dislocation line, in turn, indicates that there are obstacles to the movement of the dislocation in the material. This means the threshold stress to initiate the dislocation movement could be very probable. In such a way, the dislocation line shape can affect the yield strength of the metal or alloy. The interaction of thermal fluctuation with a dislocation is considered as kind of ‘push’ into the dislocation of an atom in thermal motion. The dislocation-line shape under thermal-fluctuations’ action is determined by the discrete dislocation dynamics method and in the form of an analytical solution of the differential equation for an elastic string with fixed ends. The standard deviation of dislocation-line points from the straight line and the averaged bulge length under thermal fluctuations action, determined by discrete dislocation dynamics and the analytical method, correlate well with each other, confirming the reliability of the modelling results. The standard deviation increases in proportion to the square root of the dislocation-line length at constant temperature and is also proportional to the square root of the temperature at constant dislocation-line length. The averaged bulge length, which determines the critical dislocation-segment length, is directly proportional to the dislocation-line length at constant temperature and does not depend on temperature at constant dislocation-line length.