Three experiments investigated whether the similarity of relational structures influences the interpretation of spatial representations. Adults were shown diagrams of hand gestures paired with simple statements and asked to judge the meaning of new gestures. In Experiment 1 the gestures were paired with active declarative statements. In Experiment 2, the gestures were paired with conjunctive and disjunctive relations. Experiment 3 used statements similar to those used in Experiment 1, but eliminated the initial object-to-object mapping provided in Experiments 1 and 2. In all three experiments, most participants chose an interpretation that set up a parallel relational structure between the gesture and its meaning: spatial elements were paired with conceptual elements and spatial relations were paired with conceptual relations. These results are consistent with the hypothesis that similarity of relational structures influences spatial reasoning, and have implications for analogical reasoning, diagrammatic reasoning, and language processing.