Abstract: A process for machining mechanical parts, including the milling of parts having a complex shape, includes the steps of determining the volume of the part to be machined, defining a corresponding machining grid, plotting the machining grid defined for the volume of the part to be machined, programming the plotted machining grid, and machining the part, grid line by grid line, according to the established programming. The process is implemented with an apparatus including a machining head coupled with a tool support. The tool support for the machining head (e.g., a cutting tool head) is positioned to face a predetermined point of the grid line to be machined, and immobilized. The machining head is mobilized to machine the desired grid line, with the tool support remaining fixed.