This paper gives a comprehensive description of the breakaway of a dislocation from a row of equally spaced pinning points, under the combined action of stress and temperature, within the model of Teutonico, Granato, and Lu¨cke (TGL). The method is to obtain an algebraic solution, for a general pinning force, using, in turn, the continuous‐pinning approximation of TGL and the ``independent‐joint approximation''; the conditions of validity of these approximations are investigated in detail. For &bgr;«1, the pinning is effectively continuous; here, &bgr;=LcU0/Cr2, whereLcis the distance between pins,U0is the maximum binding energy between a dislocation and a pin,Cis the tension of the dislocation, and the pinning force has its maximum at a displacement of orderr, the ``range.'' For &bgr;»1, the independent‐joint approximation holds (except near the mechanical breakaway stress). Then major breakaway (breakaway from the whole row) is activated at a single pin down to the stress &sgr;s= (4CU0/b2Lc3)1/2, wherebis the Burgers vector. As the stress drops further, a saddle configuration still exists for breaking the first pin, but the dislocation must surmount higher saddle points to break subsequent pins. Major breakaway is activated over an increasing number of pins as the stress decreases, and for &sgr;«&sgr;sthe pinning becomes ``quasicontinuous.'' A paradox encountered by TGL is thus resolved.