A stiffness requirement for high speed milling machines is determined by examining the stiffness of current generation high speed spindles. The desire for stability against chatter dictates that the stiffness of the machine structure and drives, when reflected to the tool tip exceed the spindle/tool holder/tool stiffness. The stiffness characteristics of a classical serial machine tool designed expressly for high speed milling are shown. Another potential design for high speed machining applications, the parallel kinematic or hexapod structure is also examined. It is found that hexapod structures exhibit lower structural stiffness than can be achieved in serial machines when using the same drive components. Furthermore, the stiffness of the hexapod structure varies widely across the workspace, leading to difficulties in control and limiting the achievable accuracy. Theoretically derived stiffnesses are compared with experimentally measured stiffnesses for two hexapod machines and are found to show good agreement.