A bi-directional valve assembly, including valves for use in closed-ended catheters or other elongate tubular devices, is disclosed. In one embodiment, a catheter assembly for insertion into a body of a patient is disclosed and comprises an elongate catheter tube including an outer wall that at least partially defines at least one lumen that extends between a proximal end and a closed distal end thereof. The catheter tube includes a valve assembly that in turn includes a linear slit valve defined through the outer wall of a distal segment of the catheter tube, and a deformation region. The deformation region includes a compliant segment disposed in the outer wall of the catheter tube and a thinned portion of the outer wall. The compliant segment and thinned portion of the deformation region cooperate to preferentially deform the outer wall and open the slit valve during aspiration through the catheter tube.