Disc prostheses, particularly for use in the lumbar region of the spine are provided. The disc prosthesis includes a core of elastomeric material provided within an inner component of fabric. The inner component is provided within an outer component of fabric. By providing a smooth inner contact surface between the inner component and the core, movement between the inner and outer components is facilitated in preference to movement between the inner component and core. Core abrasion is thus avoided. The use of an inner component and an outer component also means that the characteristics of each can he optimized to meet different aims.