As arteries carry oxygenated blood from heart to other parts of the body,the blood in it flows at a high pressure.So arteries need to have thick and elastic walls.Otherwise it may burst.If you keep your thump on your wrist ,you can feel the throbbing of arteries(known as pulse). It is felt as blood flows through it at a high pressure.

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Arteries have thick and elastic walls because the blood flows through them at a great pressure and therefore they have thick and elastic walls