The concepts of the interaction of a homogeneous electric field with a periodic quasi-one-dimensional system are discussed. The translational periodicity in the presence of the electric field is demostrated using a transformation of the Hamilton operator. The periodic perturbation Hamiltonian is introduced into the ab initio Hartree-Fock crystal orbital method and the generalized hermitian eigenvalue problem is solved with a self-consistent iteration procedure. Calculations of the static polarizability of an infinite water chain as a model and of polyyne are performed and compared with results reported in the literature.