Understanding how shallow magma is emplaced within volcanoes is crucial for hazard assessment. The 2002--2003 Stromboli eruption provides the opportunity to investigate shallow magma emplacement resulting from orthogonal feeder dikes and its possible effects. Stromboli erupted in 2002--2003, when effusive activity replaced Strombolian activity. On December 28, a NE-SW fissure propagated from the lava-filled northernmost summit crater. On December 29, a NW-SE fissure propagated north of the craters, feeding NW-SE aligned vents. On December 30, this area collapsed, reaching the sea and generating a tsunami. In mid February 2003, the NW-SE fissure became inactive, while the NE-SW effusive fissure continued until July. A model for shallow magma emplacement is proposed. The lateral propagation of a NE-SW dike from the northernmost crater was triggered. Below, a NW-SE dike, propagating from the magma-filled NE tip of the NE-SW elongated conduit, fed the NW-SE aligned vents. In February, the conduit periphery became solidified, freezing the NW-SE dike, and the transport of magma was limited to the central part, focusing its rise below the craters. This fed the NE-SW fissure until the supply decreased further (July), returning to the ordinary level sustaining Strombolian activity. Orthogonal dike emplacement followed the trajectories of the maximum (gravitational) stress σ1, partly controlled by the irregular topography of the uppermost edifice. The emplacement of orthogonal dikes in a limited area is feasible at non-perfectly conical active volcanoes, where the maximum gravitational stress may show variations from a purely radial path.