We perform numerical simulations of dynamic rupture propagation on a plane in a model consisting of two different elastic half spaces connected via a planar frictional interface governed by regularized Coulomb friction. Therefore, ruptures in this study are purely driven by the presence of a material contrast. Ruptures are nucleated on the fault using a circular symmetric expanding increase of pore‐pressure in a limited source region. We show how a wrinkle‐like rupture pulse can mature also in the 3D case where we have a mixing of in‐plane and anti‐plane modes, the instability specific of a bimaterial interface acting only for the in‐plane mode. The pulse develops inside a cone‐shaped region with its axis aligned with the direction of displacement in the softer material, its tip being at the nucleation region.