Magmatic dykes transport magma to the Earth's surface, sometimes causing eruptions. We advanced a model of dyking, treating it as plastic deformation in a porous medium, unlike the classic model that treats dykes as fractures in elastic solids. Comparing the two, we found the plastic model aligns with the fracture model in dyke speed and energy consumption, despite quantitative differences. This new method could be a powerful tool for understanding volcanic processes during tectonic activity.