Dikes and sills represent an important component of the deformation history in volcanic systems, but unlike dikes, sills are typically omitted from traditional paleostress analyses in tectonic studies. The emplacement of sheet intrusions is commonly associated with mode I fracturing in a low deviatoric stress state, where dilation is perpendicular to the fracture plane. Many natural examples of sills and dikes, however, are observed to accommodate minor shear offsets, in addition to a component of dilation. Here we present mechanical models for sills in the San Rafael Subvolcanic Field, Utah, which use field-based measurements of intrusion attitude and opening angles to constrain the tectonic stress axes during emplacement, and the relative magma pressure for that stress state. The sills display bimodal dips to the NE and SW and consistent vertical opening directions, despite variable sill dips. Based on sill attitude and opening angles, we find that the sills were emplaced during a phase of NE-SW horizontal shortening. Calculated principal stress axes are consistent (within ~4°) with paleostress results for penecontemporaneous thrust faults in the area. The models presented here can be applied to any set of dilational structures, including dikes, sills, or hydrous veins, and represent a robust method for characterising the paleostress state in areas where other brittle deformation structures (e.g. faults) are not present.