The mobility of misfit dislocations in semicoherent Cu/Ni and Cu/Ag interfaces is determined by molecular dynamics and elastic band simulation methods. Cube-on-cube oriented Cu/Ni and Cu/Ag systems were studied with the interfaces parallel to (010). Core structures of misfit dislocations in semicoherent interfaces are found to be quite different in these systems. In Cu/Ni the misfits have very narrow cores in the plane of the interface. Consequently, the shear stress to move these dislocations is large, ∼1.1 GPa. The core width and hence the misfit mobility can be changed by placing the misfit away from the chemical interface. Placement of the misfit oneatom layer into the Cu increased the core width a factor of 1.6 and lowered the threshold shear stress to 0.4 GPa. The misfit dislocations in Cu/Ag interfaces, on the other hand, are wide and therefore are much more mobile. The threshold shear stress for misfit movement in Cu/Ag is very low, ∼0.03 GPa.