Apparatus are provided for accessing and/or removing material from a body lumen. The apparatus includes a tubular sheath including a shaft having a proximal end and an expandable distal end that is expandable between a collapsed configuration and an expanded, tapered configuration. In one embodiment, the expandable member include inner and outer membranes attached together and to the shaft. Optionally, the inner membrane may include a reinforcement layer and/or the outer membrane may have a longer chord length than the inner membrane, to enhance the expandable member expanding such that a distal opening is defined by the expandable member having s a relatively large diameter tapering proximally to a lumen of the shaft. Optionally, the apparatus may include a dilator and/or one or more treatment devices receivable in the lumen of the shaft.