Properties of the large acoustic polarons in discrete molecular chains have been investigated within the adiabatic approximation. It turns out that practically all the polaron features are determined by the single parameter-coupling constant which represents the ratio between the small polaron binding energy and the electron bandwidth. Three different types of stationary solutions were found corresponding to weak, intermediate, and strong coupling limits, respectively. In the weak coupling regime, that is, for the values of coupling constant exceeding the limit of the applicability of continuum approximation but lower than the critical one ( ), we observe symmetric bond-centered solution corresponding to the polaron positioned in the middle between the adjacent lattice sites. When coupling constant overgrows, this critical value transition toward the site-centered state occurs. It takes place continuously through the intermediate asymmetric state whose position gradually approaches lattice site as coupling constant increases. One of the main consequences of the lattice discreteness is the emergence of the periodic potential, Peierls-Nabarro potential relief, through which polarons have to pass to transfer along the chain. The conditions for the polaron propagation are formulated in terms of the threshold velocity. © 2012 Wiley Periodicals, Inc.