A support device or clamp connects to a soft, flexible tube, such as a medical line, to hold the tube in an open condition. The device includes a flexible body with interengaging structure that biases the body into a desired shape when in a closed position or condition. The desired shape generally matches the outer shape of the medical line. An adhesive is disposed on the support device so as to contact the secured portion of the medical line to inhibit the walls of the line from collapsing or creasing. The support device may include base structure that has an adhesive lower surface for attaching the support device to a patient's skin.