We present analogue experiments on dike propagation in gelatin, on which we base a numerical model of horizontal and vertical growth. Experimental results show that vertical growth dominates when buoyancy becomes significant and, beforehand, the growth rates are similar. In both experimental and numerical models, influx at the base of the dike drives vertical and horizontal propagation, as well as inflating in the thickness dimension, and the proportion of vertical to horizontal growth depends on buoyancy. The model is defined for different conditions in a homogeneous medium: influx-controlled dikes dominated by fracture pressure; those dominated by viscous pressure drop; and pressure-controlled dikes. In all cases, the ratio of vertical to horizontal propagation is proportional to the ratio of buoyancy pressure to source pressure, in which buoyancy drives vertical propagation. We test the numerical model on nine dikes observed at Piton de la Fournaise from 2000 to 2003. The results show that the final dimensions and average propagation velocity can be accurately reproduced using magma-crust density differences of 50 to 300 kg/m^3, viscosities of 30 to 300 Pa*s, influxes of 50 to 750 m^3/s and shear moduli of ~10 GPa, depending on the event, with variation associated to the observed propagation velocities. The modeled magma and host rock parameters agree with previous studies, while the flux is higher than what is typically observed during eruption.