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Inside the finite element framework of LAGAMINE code, the contact conditions are introduced with specific two‐node interface elements and four‐node quadrangular elements or four‐node one point quadrature elements. A non‐associated flow rule is involved for sliding unilateral contact modelling. Two methods of penalty factor computations in the penalty contact algorithms are presented. These methods are then used for contact modelling of two isothermal examples: axisymmetric tube expansion and asymmetric slab bending, the material bulk constitutive equation being isotropic and elasto‐plastic.