Formation of isolated chips in high-speed machining is simulated by Eulerian solution. The machining includes large deformation, material failure, and contact of a tool with a workpiece; therefore, its simulation is a challenging problem. The Eulerian solution is attractive to overcome the above difficulties because the computational meshes are fixed in space and new free surfaces can be generated without a special algorithm. The present work focuses on the simulation of the isolated chips involving material failure due to shear bands. The shear-localized isolated chips in the high-speed machining, which correspond with an actual experiment, can be simulated by the Eulerian solution.