The present work is concerned with projective prepositions, which express the relation between two objects by referring to a direction in three-dimensional space. The projective prepositions have been regarded as expressing simple schematic relations of a geometric nature. A theory of the apprehension of projective relations can account for their meanings when they express strictly geometric relations. However, many studies have shown that the appropriateness of the prepositions also depends on the functional relation between the objects and that a number of functional factors influence the comprehension of English prepositions. This experimental study investigates if the acceptability of the Swedish prepositions över, under, ovanför and nedanför are influenced by functional factors as well, and whether acceptability judgments about över and under are more sensitive to functional influences than judgments about ovanför and nedanför, as has been shown for the corresponding English prepositions over and under, and above and below, respectively. It also investigates how the shapes and the parts of the related objects influence their functional interaction, and how the acceptability of the prepositions is in consequence influenced by the shapes of the objects. It was found that the theory of apprehension can indeed account for the acceptability of the prepositions when the relation between the objects is strictly geometric. It was further found that acceptability judgments about them are influenced by functional factors in a similar manner to the corresponding English prepositions when the objects are functionally related, although judgments about under and nedanför are not differentially influenced by these factors. Furthermore, the shapes and the parts of both of the related objects influence acceptability judgments about the prepositions in predictable manners. An extension of the theory of apprehension is suggested which can account for the functional influences indicated in the present study.