Edging of slab is an important process to reduce or control width in the roughing stand of hot strip mills. Simulation of the edging process was performed by the rigid viscoplastic FEM. Shifted incomplete Cholesky decomposition of the stiffness matrix combined with the conjugate gradient method, designated the shifted ICCG method, is employed for the first time in a 3-D rigid viscoplastic FEM to solve the slab edging problem. The performance of the algorithm has been analyzed in terms of CPU time, frictional boundary conditions, shift parameter ψ, memory requirement and mesh size; the computed rolling forces are examined. The numerical calculation shows, this method can result in substantial saving in memory with the potential to permit use of a smaller machine but requires a large increase in CPU time. It is shown, however to be effective for the solution of a problem such as that of the simulation of the slab edging process by the 3-D rigid viscoplastic FEM.