In the framework of the FCC study, the Nb3Sn technology plays a crucial role for high-field superconducting magnets. The new generation Nb3Sn cable greatly contributes to bring the magnetic field produced by the superconducting dipole magnets to the 16 T level; nevertheless, its mechanical properties are unknown making it difficult to predict the mechanical behaviour of the magnet structure. For this reason, an extended experimental campaign on specimens made from a stack of 10 Nb3Sn cables was launched at CERN. The 10 stack can be considered a representative sample of the magnet coil because it is produced following the same construction process: curing, reaction and impregnation. The experimental campaign consists of compression tests along the three sample directions at room temperature. Multiple loading and unloading cycles were performed as occurs for real magnet coils. A dedicated test bench was designed to measure the vertical and lateral deformations of the sample. This work presents the features of the experimental setup and the stress-strain relationships. The experimental results show a not linear elastic behaviour of the cable stack and its stiffness is strongly depended by the stress level in all loading directions. Moreover, the transverse-longitudinal strain relationships give further information about the complex behaviour of the Nb3Sn cable stack because cables slipping phenomena can be observed.