An Eulerian hyperelastic-plastic algorithm for several materials is presented. The general framework is a second order accurate Lagrange+remap scheme with dimensional splitting. The deviatoric Cauchy stress derives from the equation of state (EOS) suggested by Titarev et al. , while the isotropic pressure may be given in arbitrary, tabular or analytical form. The matrix-update of the Almansi strain during the Lagrange step is formulated compatibly with the cell volume change and time-averaged motion of cell edges. Numerical examples are given.