Spatial reasoning, where novel spatial relationships are inferred based on trained relationships, can be conceptualized as arbitrarily applicable spatial relational responding. Here, we conducted two experiments to develop and validate, for the first time, a laboratory procedure to establish arbitrarily applicable spatial relational responding in adult humans. In Experiment 1, participants were trained on nonarbitrary spatial relational tasks designed to establish contextual cues for left of, right of, above, and below. Contextual cues were then used to train a series of arbitrary spatial relations involving four abstract shapes. Following training in a subset of arbitrary relations (A is left of B, B is above C, C is right of D), subsequent testing examined the emergence of untrained spatial relations (B is right of A, C is below B, D is left of C, D is below A and A is above D). When absent in initial tests, spatial relational responding was facilitated by a remedial training procedure incorporating nonarbitrary relational guidance. Participants showed patterns of spatial relational responding consistent with test relations. In Experiment 2, a variant reversal design yielded predictable, reversed spatial relational responses. Overall, the present procedures represent the first empirical demonstration of arbitrarily applicable spatial relational responding and thus, arguably, the first functional analytic model of spatial reasoning.