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We describe an algorithm for the numerical resolution of elasto-plastic deformations in the context of antiplane shear models. The algorithm is a secondorder Godunov method. For these models the eigenvalues associated to the hyperbolic system are discontinuous. We test the algorithm on several examples. We also describe an algorithm for the resolution of the corresponding Riemann problems.doi:10.1090/qam/1276239 fatcat:ldi6bxp2krdmbbjt6xhujkt7mq