Six subjects were asked to read and try to understand the first part of Einstein’s 1905 paper on special relativity. On the basis of the diagrams drawn by the subjects while they read the text, their thinking aloud protocols, their responses to questions, and other observations, we have inferred the processes they used to understand the paper, and the role that mental images (mental representations) and their paper-and-pencil drawings played in achieving the understanding. In particular, we discuss the characteristics of the representations the subjects formed and the processes they used to form them, as well as the ways in which they derived or reached an understanding of the equations of relativity, using the mental images to assist them. From our analysis we infer that subjects translating the natural-language text into images are able to manipulate, control, and observe these representations to run simple "mental experiments," and by these means draw out the qualitative and quantitative implications of the text. The mental representations and drawings appear to mediate between the initial natural language text and the final equations. In no case did any subject achieve an understanding of the equations without using this kind of intermediate representation.