Extension of a crack on the interface between media in a structural bi-material is under consideration. Under tension applied at infinity, the mode I fracture is implemented. For analytical examination of fracture process, the modified Leonov-Panasyuk-Dugdale model is applied together with the Neuber-Novozhilov approach. Numerical modeling of the plasticity zone in a bi-material under quasi-static loading conditions has been made. In the numerical model, the updated Lagrangian definition of solid mechanics equations are used. Applying the finite element method, the plasticity zone in the vicinity of crack tip has been calculated. It has been shown that the shape of a plastic zone in bi-metal differs from that in a homogenous medium. Good agreement of numerical experiments with the proposed analytical model of a pre-fracture zone in the weakest material has been established.