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Delamination of bimaterial composed of two structured materials is considered. A crack is located at the interface between two media. Under tension applied at infinity, I mode fracture is implemented. The improved Leonov-Panasyuk-Dugdale model (LPD model) is proposed to be applied in combination with the Neuber-Novozhilov approach. The case when elastic material characteristics are identical and strength ones essentially differ is analyzed in detail. Analytical description of plotting the fracture diagram of quasi-brittle bimaterial for the plane stress state is given. Numerical modeling of the plasticity zone in bimaterial under quasi-static loading has been performed. The updated Lagrange formulation of solid-state mechanics equations is used in a numerical model. This formulation is most preferable for modeling of bodies made from elasto-plastic material subjected to large strain. Using the finite element method, a plastic zone in the vicinity of a crack tip has been described. It is shown that the shape of the plastic zone in bimetal essentially differs from that in a homogenous medium. Numerical experiments are in good agreement with the proposed analytical model of the pre-fracture zone in the weakest material.