The fluid mechanics of dike emplacement are analyzed using the translatory wave theory. The stress strain relations in the host rock are assumed linear and the fracture resistance of the host rock is assumed small. The resulting model is a flowing dyke progressing upwards to the surface with constant speed and a very small side slope. Apart from the topmost section, the form of the dyke is very close to the static form corresponding to the magma pressure in a no-flow situation. Two scales are found that control the flow, a width scale and a composite stiffness parameter for the host rock, representing the properties of the rock and the magma such as elasticity and viscosity. The theory explains a number of special features for dykes that are already known by researchers. It also adds two new points, the most interesting being that the composite stiffness of the rock can be estimated from field observations of the downwards widening angle of the dyke.