Machining of microholes in thin wires is presented to manufacture the microdevices. A machine tool was developed to machine 0.1–0.15 mm diameter holes in 0.3 mm diameter titanium alloy wires with drills or end mills. In order to realize high stiffness and damping of the workpiece holding, the workpiece inserted into a polyurethane tube was clamped on a groove of a machine table. Blind and through holes were machined with controlling the position, the orientation, and the inclination of the holes. The cutting forces were measured in drillings of 0.1 mm diameter through holes and in milling of the inclined holes with a piezoelectric dynamometer. The damping effect of the polyurethane tube support appears in the dynamic components in the cutting force. The cutting forces were also simulated to discuss the effect of the tool positioning error with respect to the workpiece axis on the cutting force in an analytical force model. The X and Y components at engagement and exit of the tool increase with the positioning error. The positioning error should be reduced to improve the machining accuracy without the tool breakage in this operation.