We investigate the effect of magmatic reservoir pressure on the propagation of dikes that approach from below, using analogue experiments. We injected oil into gelatin and observed how dike propagation responded to the stress field around a pressurized, spherical reservoir, filled with water. The reservoir was modeled using two different setups: one simply using an inflatable rubber balloon and the other by constructing a liquid‐filled cavity. We find that the dike's response is dependent on the sign of the reservoir pressure (i.e., inflated/overpressurized and deflated/underpressurized) as well as on the dike's initial orientation (i.e., if its strike is radially, circumferentially, or obliquely oriented to the reservoir). Dikes that are initially strike radial respond, respectively, by propagating toward or away from overpressurized or underpressurized reservoirs, taking advantage of the reservoir's hoop stresses. Otherwise‐oriented dikes respond by changing orientation, twisting and curling into a form dictated by the principal stresses in the medium. For overpressurized reservoirs, they are coaxed to propagate radially to, and therefore approach, the reservoir. For underpressurized reservoirs, they generally reorient to propagate tangentially, which causes them to avoid the reservoir. The magnitude of reservoir pressure controls at which distance dikes can be affected, and, at natural scales, we estimate that this occurs within a radius of a few tens of kilometers. This diminishes with time, due to viscous stress relaxation of the crust, which will occur on a timescale of hundreds of years.