Resonant transmission of deuterons through a chain of target deuterons in a metal matrix has been suggested as an explanation for the cold fusion phenomena. The fusion rate in such transmission resonance models is estimated, and the basic physical constraints are discussed. The dominating contribution to the fusion yield is found to come from meta-stable states. The fusion rate is well described by the Wentzel-Kramer-Brillouin approximation and appears to be much too small to explain the experimental anomalies.