International audienceAn approach to improve the geometrical representation of surfaces with the eXtended Finite Element Method is proposed. Surfaces are implicitly represented using the level set method. The finite element approximation is enriched by additional functions through the notion of partition of unity, to track material interfaces. Optimal rate of convergence is achieved with curved geometries, using linear elements and linear level set in elements. In order to accelerate the convergence, the order of approximation shape functions is increased, while keeping the same computational mesh. The level set is represented on a finer sub-mesh than the finite element mesh. A special attention to integration procedure is necessary. A new enrichment function is introduced to represent the behavior of curved material interfaces. Numerical examples including free surfaces and material interfaces in 2-D linear elasticity are presented to study convergence rates

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