Accurately modelling the behavior of particles circulating in accelerators is a computationally demanding task. The particle tracking code currently in use at the SSC is based upon a ‘‘thin element’’ analysis (TEAPOT). In this model each magnet in the lattice is described by a thin element at which the particle experiences an impulsive kick. Each kick requires approximately 200 floating point operations (‘‘FLOP’’). For the SSC collider lattice consisting of 104elements, performing a tracking of study for a set of 100 particles for 107turns would require 2×1015FLOPS. Even on a machine capable of 100 MFLOP/sec (MFLOPS), this would require 2×107seconds, and many such runs are necessary. It should be noted that the accuracy with which the kicks are to be calculated is important: the large number of iterations involved will magnify the effects of small errors.