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In rift settings, lateral magma propagation is commonly observed, as extensional tectonics tend to favor dyke opening perpendicular to the minimum compressive stress aligned with rift axis. Whether such intrusions propagate vertically or laterally within the crust toward eruption depends on the competition between buoyancy-driven ascent and stress-controlled fracture propagation. However, the role of the mechanical properties of the host rock, magma buoyancy, tectonic stress and surface loading in dyke propagation remain insufficiently quantified. To better understand these controlling mechanisms, a series of analogue experiments are performed by injecting a finite volume of silicone oil, analog to viscous magma, into gelatin of different compositions, analog to elastic crust subjected to surface loading and an extensional stress field. The physical properties of gelatin (density and rigidity) are measured and the shape and position of the oil crack are tracked over time using cameras. These experimental observations are further compared with stress fields computed using finite element numerical models implemented in COMSOL Multiphysics based on the experimental boundary conditions associated with applied extension and surface loading. The results indicate that, within the propagation plane, the direction of propagation consistently aligns with the direction of the maximum pressure gradient, depending on both buoyancy and the external stress field, rather than being strictly vertical as if it were entirely controlled by the buoyancy effect. The close agreement between experimentally observed trajectories and numerically derived stress-gradient paths highlights that at shallow depths, the influence of the edifice's load dominates tectonic extensional stresses at a radial distance from the volcanic summit on the order of the edifice's radius; beyond this distance, the extensional stress dominates the stress induced by the edifice's load on magma propagation. The presented findings are very important for rift volcanoes, like Nyiragongo volcano in the East African Rift, where lateral magma migration under extensional stress is potentially hazardous to the densely populated cities of Goma in the Democratic Republic of Congo (DRC) and Gisenyi in Rwanda.