A crack perpendicular to, and initially with the tip on, a bimaterial interface is studied. An asymptotic analysis is performed and crack growth proceeds straight ahead at constant remote load. Mode I conditions and plane strain are assumed. The materials on both sides of the interface are elastic perfectly-plastic with different elastic properties and the same yield stress. A finite element analysis is made and crack growth is simulated by an element relaxation technique. Because of the interface, the crack-tip driving force is not constant, which is reflected in the near-tip state. The development of the plastic zone and the crack opening displacements is presented for different elastic mismatches. Small scale yielding like results are obtained after a crack extension of about the plastic zone size from the interface, i.e. long before a square-root singular stress field may be expected to embed the plastic zone. An important observation is that the development of the crack opening displacement at the initial stage of growth is reversed when plasticity is introduced, as compared to the prediction by an elastic model. A region of stable crack growth is identified at the initial phase of growth into a stiffer material, solely due to elastic mismatch