A laser-based technique for finishing axisymmetric parts is presented which allows the efficient finishing of polymers and ceramics without tool wear, tool breakage, or cutting forces. In this process, a laser beam impinges tangentially onto the surface of a cylindrical workpiece. A flexible machine tool can be developed to grind parts of differing geometries and materials by changing process parameters instead of setups or machines, as well as integrate primary machining and secondary finishing in one machine tool. The precision of laser finishing can be enhanced by using oblique beam impingement angles. Initial results show that R a values less than 1 μm can be achieved on PMMA workpieces with a fixed beam. This paper presents the elements of the laser machine tool and preliminary results on parametric dependencies for laser finishing of polymer workpieces.