The operator of a homogeneous electric field acting on a periodic quasi-one-dimensional system can be decomposed into a sum of two terms. One term affects interband mixing of states with the same quasimomentum k and therefore describes the polarization of the electronic distribution due to the electric field. The second part causes a change in the quasimomentum k and hence is responsible for the acceleration of the electrons. While this latter term of the potential is divergent, the first term is invariant under a translational symmetry operation. This property is used to derive a homogeneous non-Hermitian system of equations to calculate the energy bands and the crystal orbitals of the periodic infinite chain in the presence of the electric field. The system of equations is solved with the help of an iterative self-consistent-field procedure. The occurrence of numerical problems, e.g., the band crossing and the undetermined phase factor of the Bloch function, is discussed and ways in which they can be solved are indicated. Finally, the method is applied to calculate the elements of the (hyper)polarization tensors, using as input the induced dipole moment which can be computed as a function of the electric-field strength. To test the method and to select the appropriate numerical procedures, applications have been peformed for infinite chains of hydrogen, water, and lithium hydride molecules. The results of these model calculations are compared with the corresponding studies on finite molecular clusters and investigations reported in the literature.