Human reasoners have an impressive ability to solve analogical reasoning problems and they still outperform computational systems. Analogical reasoning is relevant in dealing with intelligence tests. There are two kinds of approaches: to solve IQ-test problems in a way similar to humans (i.e., a cognitive approach) or to solve these problems optimally (i.e., the AI approach). Most systems can be associated with one of these approaches. Detailed systems solving geometrical intelligence tests, explaining cognitive operations based on working memory and producing precise predictions and results such as error rates and response times have not been developed so far. We present a system implemented in the cognitive architecture ACT-R, able to solve analogously developed problems of Raven’s Standard and Advanced Progressive Matrices. The model solves 66 of the 72 tested problems of both tests. The model’s predicted error rates correlate to human performance with r = .8 for the Advanced Progressive Matrices and r = .7 for all problems together.