AbstractSaucer-shaped sills are common in sedimentary basins worldwide. The saucer shape relates to asymmetric sill-tip stress distributions during intrusion caused by bending of the overburden. Most saucer-shaped sill models are constructed using a magma-analogue excess source pressure (Po) to drive host-rock failure, but without tectonic stress. Here we present axisymmetric finite-element simulations of radially propagating sills for a range of tectonic stress (σr) conditions, from horizontal tension (σr < 0) to horizontal compression (0 < σr). Response to σr falls into four regimes, based on sill geometry and failure mode of the host rock. The regimes are considered in terms of the ratio of tectonic stress versus magma source pressure R = σr/Po: (I) initially seeded sills transition to a dike during horizontal extension (R < 0); (II) with R increasing from 0 towards 1 (compressive σr), sill base length increases and sill incline decreases; (III) where 1 < R < 2, sill base length relatively decreases and sill incline increases; and (IV) where R > 2, sills grow as inclined sheets. Sills in regimes I–III grow dominantly by tensile failure of the host rock, whereas sills in regime IV grow by shear failure of the host rock. Varying σr achieves a range of sill geometries that match natural sill profiles. Tectonic stress therefore represents a primary control on saucer-shaped sill geometry and emplacement mechanism.