Final answer:
Capillaries are the blood vessels that lack elastic tissue, as they are composed of a single layer of endothelial cells and are meant for exchange rather than carrying blood under high pressure.
Step-by-step explanation:
The blood vessels that lack elastic tissue are capillaries. Capillaries are composed of a single layer of endothelial cells and do not have the smooth muscle or elastic fibers that are found in arteries and veins. They are the sites of gas and nutrient exchange between the blood and tissues. Arteries, on the other hand, have thick walls with elastic fibers to withstand high pressure. Veins also contain some elastic fibers but less than arteries, to help maintain blood flow back to the heart aided by valves and skeletal muscle contractions.