Abstract The finite difference method with arbitrary grids for the solution of the differential equation system governing the elastic–static behavior of three-dimensional continua is developed in this paper. An in-depth examination of the various questions arising in calculating the finite difference operators, in the assembling and in the reducing of the coefficient matrix of the algebraic equation system is carried out. An iterative algorithm for optimizing the finite difference operators at every discretization point and a ‘block’ type procedure for storing and solving the algebraic equation system in the unknown displacements is furnished. An attempt is made to calculate and minimize the various errors related to the discretization process. A computer procedure based on an improvement and extension of the well-known displacement approach is given. Some numerical examples show that the proposed method provides good results and is suitable and feasible for the analysis of large structures with low discretization and computational effort.