We present a new method for solving the two-point seismic ray tracing problem based on Fermat's principle. The algorithm overcomes some well known difficulties that arise in standard ray shooting and bending methods. Problems related to: (1) the selection of new take-off angles, and (2) local minima in multipathing cases, are overcome by using an efficient simulated annealing (SA) algorithm. At each iteration, the ray is propagated from the source by solving a standard initial value problem. The last portion of the ray-path is then forced to pass through the receiver. Using SA, the total traveltime is then globally minimized by obtaining the initial conditions that produce the absolute minimum path. The procedure is suitable for tracing rays through 2D complex structures, although it can be extended to deal with 3D velocity media. Not only direct waves, but also reflected and head-waves can be incorporated in the scheme. One important advantage is its simplicity, in as much as any available or user-preferred initial value solver system can be used. A number of clarifying examples of multipathing in 2D media are examined. ¿ American Geophysical Union 1996