Abstract Based on the requirement of field engineering, we proposed a new numerical method for analyzing the solid mechanics with Euler variables. By replacing the Lagrange variables with the Euler variables, there will be three new items appearing in the equation. We use the fixed Euler grid to calculate solid mechanics, and use the boundary of material regiment to describe the movement of the boundary of material, after the boundary of material regiment moves beyond the Euler element grid size, new Euler element grids will appear and the corresponding old Euler element grids which have been out of the region of material will disappear. By this way, the movement of solid could be calculated in the Euler fixed grids. Then we did some test cases, we get the result that the new method is right and could be used to calculate the solid mechanic problems.