Micro-structured surfaces are assuming an ever-increasing role since they define the ultimate performance of many industrial components and products. Micro-channels, in particular, have many potential applications in micro-fluidic devices, micro heat exchangers, and friction control. This paper proposes an innovative vibration-assisted machining method to generate micro-channels on the external surface of a cylinder. This method, referred to as elliptical vibration texturing, was originally developed by the authors to generate dimple patterns. It uses the modulation of the depth-of-cut by tool vibrations to create surface textures. The most promising features of the proposed method are its high efficiency, low cost, and scalability for mass production. It is shown that with proper combinations of the process parameters the created dimples start to overlap and form channels. An analytical model is established to predict channel formation with respect to the overlapping ratios of the dimples. Channel formation criteria and expressions for channel geometries are given along with a channel generation map that relates channel geometry to the process parameters. Experimental results are given to verify the model. A further example of micro-pattern generation is also given to showcase the flexibility of the process.