Parametric machining is applied to fabricate micro-scale textures on surfaces by rotating the workpiece and tool. Periodic circular textures are controlled by only four parameters: the distance from the rotation center of the workpiece to that of the tool holder, the rotation radius of the tool in the tool holder, and the angular velocities of the workpiece and the tool holder. The textures to be machined are controlled by simulating the trajectory of the tool on the workpiece. A texturing machine was developed with two servomotors and three stepping motors, where the rotations of the servomotors were synchronized. Some examples are shown to verify the presented texturing in cutting tests. Because functional surfaces should be controlled by the surface structure, a model is presented to simulate the surface profiles of the textures. The orientation of the cutting tool with respect to the cutting direction is discussed in terms of the surface structure and the surface finish. The cutting load is estimated with the indentation and the shearing components in a simplified force model.