For UIC60 and UIC54 rail track, our on-site measurements, together with finite elements analysis (Thompson in Railway noise and vibration: mechanisms, modelling and means of control. Elsevier, Amsterdam, 2008 ), showed that the pin-pin resonance modes of the rail track in lateral and vertical direction (i.e. the two principal directions perpendicular to the length of rail tracks) are in the frequency ratio of around 1:2. Following our recent development of Tuned Mass Damper (TMD, Fig. 1) (Ho et al. in Tuned Mass Damper for Rail Noise Control. Springer, Berlin 2012 ), multiple masses were employed so that they oscillate along the shear direction of the resilient layers to form a multiple spring-mass system in both vertical and lateral directions. As the damping mechanism strongly relies on the stiffness of the resilient layer, thus a resilient composite material with anisotropic shear moduli in orthogonal directions can be used to tackle the issue of different pin-pin resonance modes in both lateral and vertical directions. Since the resonance frequency is proportional to the square root of the modulus, with a frequency ratio of ~2 between the vertical and lateral pin-pin resonance modes, a ratio of 4 between the shear moduli of the two respective directions is required. In this study, aligned glass fibres were embedded into silicone matrix to form uniform composite resilient layers with orthogonal shear moduli. Their shear stiffnesses were measured by a tensile tester, with the setup for shear modulus measurement based on the International Organization for Standardization ISO-1827. Our results showed that these composites can achieve an orthogonal shear moduli ratio of about 1:1.44. Vibration tests were performed to verify that two natural frequencies were observed in these TMDs using the orthogonal resilient layers, which is not possible for TMDs using isotropic resilient layer materials. Hence, resilient layer material of orthogonal shear moduli as applied in the TMD is promising for suppressing the two direction pin-pin resonance modes in rail tracks.