THE ALGORITHM DESCRIBED here is used to generate all simultaneous submodels of an econometric model. F. M. Fisher's correspondence principle [1] for simultaneous equation models requires that all simultaneous submodels of the full model be solvable by a particular form of simple iteration, and suggests that the smallest simultaneous submodels be tested first. This algorithm does that by using the primitive v cycle (hereafter called seed) description of a simultaneous equation model [2]. Using the seed description of a model, the algorithm generates every simultaneous submodel only once and its execution time is linear in the number of simultaneous submodels. That number may be very large, however, and for this reason the algorithm proceeds step-by-step, generating simultaneous submodels using previously generated submodels. In this way, only successful submodels (those which pass Fisher's iteration test) need to be used to generate more simultaneous submodels. This feature makes the application of Fisher's test practical even for very large models. The algorithm, called SIFT, is written in 360/370 assembly language. It is available on the National CSS time-sharing network which operates in the USA and Europe or from the author at National CSS, 485 Summer Street, Stamford, Connecticut 06901.