Dikes along rift zones propagate laterally downslope for tens of kilometers, often becoming arrested before topographic reliefs. We use analogue and numerical models to test the conditions controlling the lateral propagation and arrest of dikes, exploring the presence of a slope in connection with buoyancy and rigidity layering. A gentle downslope assists lateral propagation when combined with an effective barrier to magma ascent, e.g., gelatin stiffness contrasts, while antibuoyancy alone may be insufficient to prevent upward propagation. We also observe that experimental dikes become arrested when reaching a plain before opposite reliefs. Our numerical models show that below the plain the stress field induced by topography hinders further dike propagation. We suggest that lateral dike propagation requires an efficient barrier (rigidity) to upward propagation, assisting antibuoyancy, and a lateral pressure gradient perpendicular to the least compressive stress axis, while dike arrest may be induced by external reliefs.