Previous research has consistently found that spontaneous analogical transfer is strongly tied to concrete and contextual similarities between the cases. However, that work has largely failed to acknowledge that the relevant factor in transfer is the similarity between individuals' mental representations of the situations rather than the overt similarities between the cases themselves. Across several studies, we found that participants were able to transfer strategies learned from a perceptually concrete simulation of a physical system to a task with very dissimilar content and appearance. This transfer was reflected in better performance on the transfer task when its underlying dynamics were consistent rather than inconsistent with the preceding training task. Our data indicate that transfer in these tasks relies on the perceptual and spatial nature of the training task but does not depend on direct interaction with the system, with participants performing equally well after simply observing the concrete simulation. We argue that participants generated a spatial, dynamic, and force-based mental model while interacting with the training simulation and tended to spontaneously interpret the transfer task according to this primed model. Unexpectedly, our data consistently show that transfer was independent of reported recognition of the analogy between tasks: Although such recognition was associated with better overall performance, it was not associated with better transfer (in terms of applying an appropriate strategy). Together, these findings suggest that analogical transfer between overtly dissimilar cases may be much more common--and much more relevant to our cognitive processing--than is generally assumed. (Contains 4 figures and 1 table.)