An artery is made up of elastic fibers, smooth muscle and a membrane called an 'Endothelium'. There is a hole running through the center of the artery called the 'Lumen'. Artery walls need to be thick and stretchy, this is because they carry oxygenated blood at a high pressure from the heart.
A vein is also made up of elastic fibers and smooth muscle and also has an Endothelium. Veins differ from Ateries because their walls are much thinner, as the deoxygenated blood they carry is at a lower pressure. The lumen in a vein is bigger than that of an artery to allow blood to flow though it with ease. Veins also contain valves to make sure that the blood continues to flow in the right direction.
Capillaries are very small and is made up of an Endothelium that is only 1 cell thick. This allows for food, oxygen and carbon dioxide to move through the walls by diffusion.
Ref: Image from www.hcc.uce.ac.uk/physiology/images/arteries%2520
Edited by Parsons R,Undated,Double Science Biology The Revision Guide Higher Level,Newcastle upon tyne,Coordination Group Publications Ltd.