The stiffness characteristics of classical serial machine tools are compared with parallel kinematic, or hexapod, structures for high-speed milling applications. A structural stiffness requirement for this application is determined by the stiffness of current-generation high-speed spindles and the desire for stability against chatter. It is found that hexapod structures exhibit lower structural stiffness than can be achieved in serial machines using the same drive components. Furthermore, the stiffness varies widely across the workspace of hexapod machines, leading to difficulties in control and limiting achievable accuracy. Theoretically derived stiffnesses are compared with experimentally measured stiffnesses for two hexapod machines and are found to show good agreement.