The majority of work contained in this thesis involves characterisation of the mechanical losses in fused silica ribbon fibres to determine their potential for use in suspending the 40kg test masses for Advanced LIGO. The design of fibres is discussed here, demonstrating the advantages of rectangular cross sections over the circular cross sections already used in GEO600, with experimental work used to show the viability of this suspension scheme. The losses of a number of modes of oscillation of fibres were investigated using different suspension designs to reduce excess loss mechanisms. Measurements made of the material loss of the fused silica, using cantilever bending modes of a fibre held at one end, gave values slightly higher than those used in the design of noise curves for Advanced LIGO. The measurements also showed a reduced thermoelastic damping effect from that theoretically calculated from which an altered value for the Young’s modulus of the fibres was found compared to the value for bulk fused silica. Measurements performed using the violin modes and pendulum modes of the fibres showed that, while excess loss mechanisms were characterised and in the case of the violin mode measurement shown to be negligible, the level of dilution of loss calculated theoretically was not achieved. The source of increased loss is thought to be due to the energy being concentrated closer to lossy welded regions of the fibre. The losses measured for the linear pendulum were the lowest ever measured. Measurements of the vertical bounce mode of a small mass suspended between two fibres has shown clear evidence that there is no intrinsic stress dependence of the material loss of fused silica and has given further evidence that the majority of loss in the fibres comes from a thin highly dissipative layer on the surface. The strength of ribbon fibres has been shown to be sufficient to carry the working load of the Advanced LIGO masses, with a 20kg test suspension being created, however there was a wide variation in measured fibre breaking strengths thought to be due to bending in the fibre coupling longitudinal force into shear stress. Issues regarding thermal stress at welds are discussed with suggested solutions for construction of Advanced LIGO suspensions.