Medical dressings having flexible and conformable borders when attached to skin and devices such as, e.g., catheters, etc. to facilitate strong adhesive securement of the medical dressings to skin over extended periods of time. The medical dressings include a relatively low modulus backing layer paired with a relatively high modulus support material the backing layer, and a tubing slot configured to, e.g., stabilize a catheter other tubing on the skin of a patient. The backing layer may extend outwardly from the support material over a substantial majority of the perimeter of the medical dressing to form a border of adhesive material with elasticity to resist lifting from a patient's skin.
