A theory of acoustic-mode scattering has been formulated within the tight-binding approximation of band theory, and has been applied to narrow-band semiconduction in organic molecular crystals. The latter problem has been treated previously only in terms of phenomenological scattering parameters. The interaction constants are obtained explicitly as gradients of the characteristic overlap integrals. In addition, the wave-vector dependence of the matrix elements is taken into account. To first order in the (relative) displacements, the matrix elements include scattering by short-wavelength phonons, an essential feature of the narrow-band case not treated by conventional deformation-potential theory. The matrix elements physically represent variations of the band width and band centroid with relative displacement; in addition small (drag) terms proportional to the local lattice velocities are obtained. The theory is first applied to a onedimensional band model, for the case of both elastic and inelastic scattering. It is then applied to the basecentered-monoclinic structure, for which numerical estimates of the interaction constants have been made available by LeBlanc for anthracene.