To investigate the mechanism underlying the fragmentation of oceanic plates, we study the breakup of the Farallon plate into the Cocos plate and the Nazca plate, which took place 25 to 30 m.y. ago. Using finite element methods and a reconstruction of regional plate boundaries, we calculate the stress field in the Farallon plate at approximately 30 m.y. ago (just prior to the fragmentation). The resulting stress field is dominated by high tensional stresses (maximum principal stresses of 5 to 6 kbar). North-to-south tension near present-day Panama is proposed to have caused fragmentation of the Farallon plate and inception of spreading along the new Cocos-Nazca plate boundary. The plate interaction that allowed the high level of tensional stresses in the Farallon p ate is not unique for our case study, and the proposed mechanism sheds light on the problem of fragmentation of oceanic plates. The preliminary results of stress field calculations for the present-day Nazca plate show interesting stress variations along the strike of the South American trench system.