A novel rectangular-corrugated waveguide is proposed for submillimeter and terahertz vacuum devices. Two parallel corrugations that are enclosed in a rectangular waveguide create a beam channel that supports an interaction with a cylindrical electron beam. A notable advantage of the double-corrugated rectangular waveguide slow-wave structure (SWS) is the extension of well-established cylindrical beam technology to corrugated waveguide SWSs. The structure is also fully realizable with the most recent microfabrication techniques and is easily assembled. A detailed study to describe the electromagnetic behavior of the presented SWS is performed by 3-D electromagnetic simulation. A 650-GHz backward-wave oscillator and a 227-GHz traveling-wave tube are designed and simulated, by 3-D particle-in-cell code, to highlight the great potential of the double-corrugated rectangular waveguide for submillimeter frequency vacuum devices.