Hybrid Manufacturing technologies enable the manufacturability and high manufacturing efficiency of innovative part designs comprising high complexity features which could not otherwise be manufactured in a single or a small number of steps. This study proposes the design of an industrial-grade low-cost fully automated multi-axis hybrid Additive and Subtractive CNC machine for non-metallic parts. It combines operations of a six-axis CNC machining center with a six-axis extrusion 3D printer with automated tool head change for processing parts made of polymer and special 3D printing materials (e.g., carbon fiber reinforced filaments). The design process includes static, dynamic and harmonic response Finite Element Analysis to optimize its structural strength and at the same time to reduce machine component costs down to a few thousand euros for all included components and subsystems, thus making it viable for industrial purposes. In investigated loading scenarios, analysis results show that at the brim of a 200 mm diameter round machine table, even at its most unfavorable angular positions, maximum deformation was no more than 0.24 mm, with a factor of safety in the magnitude of 10 to 20 while applying cutting force profiles with amplitudes up to 100 N, which exceedingly satisfies structural specifications for the proposed machine design operation.