The insulation system is a key component of Nb3Sn superconducting accelerator magnets under construction for the LHC High Luminosity upgrade (HL-LHC). It needs to ensure the magnet operation at 1.9 K and to guarantee the functionality during the complete service life of the magnet in the accelerator under high mechanical stress and irradiation dose up to 35 MGy. A first set of experimental tests have been performed at room and cryogenic temperature to confirm the stress-strain behaviour, the mechanical strength and the failure mechanisms of the cable insulation system used for the HL-LHC Nb3Sn accelerator magnets. CERN is performing tensile and inter laminar shear strength (ILSS) tests and a non-standardized combined compressive shear test, which is more representative for magnets operational conditions. The tested samples consists of the same raw insulation material and follow similar specific manufacturing procedures as the ones of the 11 T Nb3Sn dipole and the MQXF Nb3Sn quadrupole magnets. In order to represent the different design criteria of these magnets, the sensitivity to the mechanical behaviour of the CTD-101K resin impregnated samples to a varying S2-glass yarn density, sizing and fibre volume fraction was investigated with different types of samples as well as the effect of mica used in the insulation system.