A tubular conduit is used to access blood vessels or other structures in the human body. The conduit has a distal tip angled to match the angle of entry into the body and an end contour adapted for the surface of the target vessel or organ. The contour may be curved to match the curve on the outer surface of the vessel or organ. The conduit's angled and contoured distal end may be adapted to engage, and align the conduit with, the surface of the vessel or organ. The conduit bears a longitudinal groove along its lower, inner surface. When the conduit is appropriately aligned, the groove may be used to guide a needle tip to the desired location, for example, the mid-line of the vessel or organ.