A flexible fire resistant innerduct structure is configured to contain a cable within a conduit. The innerduct structure includes a pair of adjacent strip-shaped layers of flexible material that are joined along their longitudinal edges to define a channel through which the cable can extend longitudinally through the innerduct structure between the layers. The adjacent layers have differing widths between their longitudinal edges, whereby the wider layer bulges away from the narrower layer to impart an open configuration to the channel. Other features of the innerduct structure relate to the material of which it is formed. Such features includes the structure of the material, such as a woven structure, and further include properties such as melting point, tensile strength, fire resistance, elongation, coefficient of friction, crimp resistance and compression recovery.