A finite field approach for the calculation of static vibrational polarizabilities of molecules is extended to polymers using the previously developed method for the calculation of the electronic contribution of periodic quasi-one-dimensional systems. The method has been applied to study the effect of the vibrations on the static polarizability of an infinite stack of alternating HF molecules and of poly(HF) in the experimentally determined hydrogen-bonded zig-zag structure. The results are discussed and compared with a calculation for the isolated HF molecule and studies in the literature.