Sills are concordant sheet-like bodies of magma. Their mechanics of emplacement is an important but still not fully understood topic. The well-exposed basaltic Njardvik Sill in the extinct Tertiary Dyrfjöll Volcano in Northeast Iceland offers exceptionally clear insights into the mechanism of sill emplacement. The sill is multiple and consists of at least 7 units (sills) all of which were emplaced along a sharp contact between a rhyolitic intrusion and adjacent basaltic lava flows. Each sill unit was supplied with magma from an inclined sheet. The contacts between the sheets and the sill units are very clear and show that the sill units are much thicker than their feeder sheets. Since the Njardvik Sill consists of separate units, it obviously did not evolve into a homogeneous magma body. Nevertheless, the abrupt change in dip and thickness from inclined sheets to horizontal sills at this particular locality indicates that the earlier sills were influencing the stress field in their vicinity during the subsequent sheet injections. The local stresses around the newly formed sill units forced each of the subsequently injected sheets to change into sills. The Njardvik Sill can be followed laterally in a coastal section for 140 m until it ends abruptly at a fault that cuts the sill. Using these field observations as a basis, a numerical model shows how an inclined sheet opens up the contact between the felsic intrusion and the basaltic lava pile, along which the sill emplacement takes place. The results suggest that sill emplacement is primarily the result of stress rotation at contacts between layers of contrasting mechanical properties. There, the orientation of the maximum principal compressive stress σ1 is horizontal. Hence, such contacts can represent interfaces along which sill emplacement is encouraged.Once a sill has been emplaced, it extends the stress field with a horizontal orientation of σ1. Consequently, inclined sheets and dykes injected near the sill will be deflected into sills. The injection frequency of further sill units controls if the sill can grow into a larger magma body by mixing of the newly supplied with the initially injected magma. In case of the Njardvik Sill, the injection frequency was low, so subsequently emplaced sill units can be distinguished. The contacts between the sheets and the sill units are very clear and show that the sill units are much thicker than their feeder sheets. Since the Njardvik Sill consists of separate units, it obviously did not evolve into a homogeneous magma body. Nevertheless, the abrupt change in dip and thickness from inclined sheets to horizontal sills at this particular locality indicates that the earlier sills were influencing the stress field in their vicinity during the subsequent sheet injections. The local stresses around the newly formed sill units forced each of the subsequently injected sheets to change into sills. The Njardvik Sill can be followed laterally in a coastal section for 140 m until it ends abruptly at a fault that cuts the ...