The sliding of charged solitons in heavily doped trans-polyacetylene is investigated by undertaking a molecular dynamics simulation with a charged model molecule. The saturated soliton sliding speed is determined so that the period of the passing solitons achieves a constant value, i.e., 15 fs. A mechanism is proposed where coupling occurs between the passing solitons and the C–C stretching vibration. This coupling determines the saturated sliding speed. As the accumulated energy of the C–C stretching vibration is effectively used for the soliton lattice translation, the speed becomes stable, and coherent sliding occurs. A comparison of (CH)x with (CD)x shows that the C–D bending mode mixes easily with the C–C stretching mode in the sliding process. The soliton sliding speed of (CD)x is not as stable as that of (CH)x. This implies that (CD)x cannot have a conductivity as high as that of (CH)x.