Beginning with her 1952 paper “Operational Definition and Analogy in Physical Theories”, Mary Hesse has championed an approach to analogy in scientific investigation that aims to capture the different ways in which analogies are used by working scientists. For various reasons, Hesse’s pioneering contribution, which culminated in her Models and Analogies in Science (1963–66), has often been misunderstood. This paper addresses what is arguably one of the most common misunderstandings of Hesse’s approach, having to do with the distinction between ‘formal’ and ‘material’ analogies in science. In response to concerns about the overly restrictive character of Hesse’s requirements on inductively strong analogical inferences, an interpretation and partial refinement of Hesse’s proposal will be provided that does justice to its significance for the epistemology of science.