The European Extremely Large Telescope (E-ELT) is a 42-m class optical telescope with a segmented primary mirror composed of 984 segments which is currently being studied by ESO (European Southern Observatory). The segment support system combines a series of mechanical whiffletrees for the axial support, a central diaphragm for lateral support and a torsional constrainer. These elements are fixed to a common moving frame which is actively moved by means of three actuators in piston and tip-tilt in order to keep the whole primary mirror in phase. The moving frame is fixed to the segments subcells, which properly attach the segments to the cell structure, by means of special flexures, allowing large axial alignment capability combined with high lateral stiffness. This paper describes the development of the support system for the primary mirror segments of the E-ELT, which has been specified for a high stiffness and eigenfrequencies, 60Hz for axial modes and 40Hz for lateral ones.