The cognitive processes in a widely used, non-verbal test of analytic intelligence--the Raven Progressive Matrices Test (J. C. Raven, 1962)--were analyzed. The analysis determined which processes distinguished between higher-scoring and lower-scoring subjects and which processes were common to all subjects and all items on the test. The analysis was based on detailed performance characteristics on the Tower of Hanoi puzzle such as verbal protocols, eye fixation patterns, and errors. The theory was expressed as a pair of computer simulation models--FAIRAVEN and BETTERAVEN--that performed like the median or best subjects in the samples of 12 and 22 college students. The processing characteristic common to all subjects was an incremental, reiterative strategy for encoding and inducing the regularities in each problem. The processes that distinguished among individuals were primarily the ability to induce abstract relations and the ability to manage dynamically a large set of problem-solving goals in working memory. Five sample test items, 3 tables, 12 figures, an appendix summarizing correct solutions by the models, and a 59-item list of references are included. (SLD)