We provide detailed observations on the shape of dikes from well-exposed field locations in the Isle of Rum, Scotland, and Helam Mine, South Africa. The basaltic Rum dikes crop out on a smaller scale than the Helam kimberlite dikes and have a smaller length to thickness ratio (∼100:1 Isle of Rum, ∼1000:1 Helam Mine). We compare the dike thickness field measurements with the geometry predicted by elastic theory, finding best-fit models to estimate magma overpressure and regional stress gradients at the time of dike emplacement. Most of the dike shapes fit poorly with elastic theory, being too thick at the dike ends and too narrow in the middle. Even for dikes where the model fit is acceptable, the calculated overpressures and stress gradients are very large and much larger than independent estimates based on rock strength, particularly for the small-scale basaltic dikes on Rum, where calculated overpressures average 687 MPa, and calculated stress gradients average 622 MPa m−1. The Swartruggens dikes have calculated overpressures of between 4 and 40 MPa and calculated stress gradients in the range of 15–87 kPa m−1. Dike shape can be explained by a combination of host-rock inelastic deformation prior to and coeval with magma emplacement, and by magma chilling at the dike's tapering edges, which prevented its closure as magma pressure declined during emplacement; this sequence provides the most complete explanation for the mismatches between the data and the model. The permanent wedging of the dike edges due to chilling has implications for crustal magma transport and strain response in the crust due to dike emplacement.