A severe plastic deformation process, termed accumulative extrusion bonding (AEB), is conceived to steady-state bond metals in the form of multilayered tubes. It is shown that AEB can facilitate bonding of metals in their solid-state, like the process of accumulative roll bonding (ARB). The AEB steps involve iterative extrusion, cutting, expanding, restacking, and annealing. As the process is iterated, the laminated structure layer thicknesses decrease within the tube wall, while the tube wall thickness and outer diameter remain constant. Multilayered bimetallic tubes with approximately 2 mm wall thickness and 25.25 mm outer diameter of copper-aluminum are produced at 52% radial strain per extrusion pass to contain eight layers. Furthermore, tubes of copper-copper are produced at 52% and 68% strain to contain two layers. The amount of bonding at the metal-to-metal interfaces and grain structure are measured using optical microscopy. After detailed examination, only the copper-copper bimetal deformed to 68% strain is found bonded. The yield strength of the copper-copper tube extruded at 68% improves from 83 MPa to 481 MPa; a 480% increase. Surface preparation, as described by the thin film theory, and the amount of deformation imposed per extrusion pass are identified and discussed as key contributors to enact successful metal-to-metal bonding at the interface. Unlike in ARB, bonding in AEB does not occur at ~50% strain revealing the significant role of more complex geometry of tubes relative to sheets in solid-state bonding.