Shear band is analyzed via Element Free Galerkin method and the result is compared with that from finite element analysis. Adequate numerical integration and size of domain of influence are sought from numerical experiment with regards to shear band analysis via EFG method. Linear polynomial basis and quartic spline weight function with circlular domain of influence are used for forming EFG shape function, and D'Alembert method is utilized for implementation of essential boundary condition. Staggered algorithm is chosen for decoupling mechanical field from thermal field. Employed are central difference method and Euler forward method in relation to integration of equation of motion and a rate constitutive equation involved.