To investigate the mechanism underlying the break-up of the Farallon plate into the Cocos plate and Nazca plate, we analyze the state of stress in the Farallon plate at about 30 m.y. B.P., just prior to the fragmentation. To this purpose we use finite element methods and a reconstruction of regional plate boundaries appropriate for 30 m.y. B.P. A key role in the model is played by the dependence of two important plate-tectonics forces (slab pull and ridge push) on the age of oceanic lithosphere. The results show a highly tensional stress field, with maximum principal stresses of 5 to 6 kbar. North-south tension in the vicinity of present-day Panama is proposed to have been the cause for the fragmentation of the Farallon plate and the inception of spreading along the new Cocos-Nazca plate boundary. Because the kind of plate interaction that gave rise to the high level of tensional stresses in the Farallon plate is not restricted to the area of this study, the proposed mechanism seems to shed light on the problem of fragmentation of oceanic plates in general.