A catheter having a selectively variable degree of flexibility includes an elongate tubular outer member and an elongate tubular inner member disposed within the outer member. The catheter further includes a cavity disposed in between the outer and inner members. A tubular braid of filaments may be disposed within the cavity. The outer and inner members are movable relative to each other along intermediate portions thereof when in a first configuration, and are not movable relative to each other when in a second configuration. When the inner and outer members are in the first configuration, the tubular braid of filaments is movably disposed relative to at least one of the outer member and the inner member. When the inner and outer members are in the second configuration, the inner and outer members clamp the tubular braid of filaments in a fixed position relative to the inner and outer members.