This article presents research into human mental spatial reasoning with orientation knowledge. In particular, we look at reasoning problems about cardinal directions that possess multiple valid solutions (i.e., are spatially underdetermined), at human preferences for some of these solutions, and at representational and procedural factors that lead to such preferences. The article presents, first, a discussion of existing, related conceptual and computational approaches; second, results of empirical research into the solution preferences that human reasoners actually have; and, third, a novel computational model that relies on a parsimonious and flexible spatio-analogical knowledge representation structure to robustly reproduce the behavior observed with human reasoners.