A solution is obtained for the case in which a sem-infinite crack suddenly appears and grows at constant velocity in a stretched elastic body. The problem, one of mixed boundary values on a half plane, is solved by transform methods including the Weiner-Hopf and Cagniard techniques. Among the graphical results presented is the time variation of the transverse stress at a fixed point on the line of fracture as the tip of the crack approaches. Asymptotic forms for the stresses near the crack tip are also obtained and are compared with results of other studies in crack propagation.