The ESRF is proceeding with the design and procurement of its new low emittance storage ring (Extremely Brilliant Source project). This completely new storage ring requires a high performance support system, providing high stability (first resonance frequency about 50Hz) and a precise alignment capability (50μm, manual in transverse direction and motorized in the vertical one). In order to meet these requirements we decided to support the magnets of each of the 32 cells of the synchrotron with four identical girders that was considered the best compromise between cost, complexity and performances. Each of the resulting 128 girders is 5.1m long, carries about seven tons of magnets, and its weight including fixed basement and adjusting system is six tons. The adjustment system relies on modified commercial wedges; their stiffness was evaluated through laboratory tests. The FEA calculations carried out to optimize the design will be presented, together with the results obtained on a complete prototype girder system which was built and extensively tested and confirmed the modal calculations.