A model of vibronic origin is used to investigate the important issue of metal-insulator transition in low-dimensional materials. For zero temperature, the stability of the single-band model chain is controlled by the competition between the internal electron-phonon coupling and the nearest-neighbor hopping integral. Assuming one particular deformation mode, one can analytically derive an instability criterion in which the band filling is explicitly included. The carrier doping directly controls the stability of a one-dimensional chain. For a half-filled band, the Peierls instability is recovered. For finite temperatures, a similar criterion is derived and can be used to investigate the metal-insulator transition temperatures. (C) 2004 American Institute of Physics.