We present a theoretical model for the shock formation that is related to coronal and interplanetary type II radio bursts associated with coronal mass ejections on the basis of the magnetic reconnection model of eruptive solar flares. Coronal type II bursts are usually observed in the metric wavelength range (metric type II bursts), and interplanetary bursts are usually observed in the decametric-hectometric wavelength range (decametrichectometric bursts). Our research shows that the decametric-hectometric type II radio bursts are produced by the piston-driven fast-mode MHD shock that is formed in front of an eruptive plasmoid (a magnetic island in the two-dimensional sense or a magnetic flux rope in the three-dimensional sense), while the metric radio bursts are produced by the reverse fast-mode MHD shock that is formed through the collision of a strong reconnection jet with the bottom of the plasmoid. This reverse shock apparently moves upward as long as the reconnection jet is sufficiently strong and dies away when the energy release of the reconnection stops or weakens significantly. On the other hand, the piston-driven fast shock continues to exist when the plasmoid moves upward. Our model succeeds in explaining the observational result that the piston-driven fast shock that produces decametrichectometric type II bursts moves faster and survives longer than the other shock.