We describe a computational model for solving problems from Raven’s Progressive Matrices (RPM), a family of standardized intelligence tests. Existing computational models for solving RPM problems generally reason over amodal propositional representations of test inputs. However, there is considerable evidence that humans can also apply imagery-based reasoning strategies to RPM problems, in which processes rooted in perception operate over modal representations of test inputs. In this paper, we present the “affine model,” a computational model that simulates modal reasoning by using iconic visual representations together with affine and set transformations over these representations to solve a given RPM problem. Various configurations of the affine model successfully solve between 33 and 38 of the 60 problems on the Standard Progressive Matrices, which matches levels of performance for typically developing 9- to 11-year-old children. This suggests that, for at least a sizeable subset of RPM problems, it is not always necessary to extract amodal symbols in order to arrive at the correct answer, and iconic visual representations constitute a sufficient form of representation to successfully solve these problems. We intend for the affine model to serve as a complementary computational account to existing propositional models, which together may provide an integrated, dual-process account of human problem solving on the RPM.