A holder or stabilizing device for medical IV or catheters having flexible tubing attached. An elongated strap-like panel made of a flexible material has an intermediate portion and a pair of attachment portions extending in opposite directions from the intermediate portion, the intermediate and attachment portions defining opposite side edges of the panel. The panel has an outside side generally visible during use. A pair of tubing-securing apertures is provided in the intermediate portion located generally adjacent respective opposite sides of the panel and across from each other, with an adhesive area on the intermediate portion on the outside side between the at least one pair of tubing-securing apertures and is positioned so as to engage the flexible tubing when passing through and extending on the outside side of the panel between the pair of tubing-securing apertures. A set of holders may be provided, color-coded to indicate particular size.