According to the American Academy of Dermatology, it is possible to get a sunburn or tan while sitting in the shade. This is because many surfaces, such as concrete, water and sand, reflect UV rays. Light rays often penetrate or filter through shade sources as well.
While sitting in the shade is safer than sitting in direct sunlight, not all shade sources are created equal. Umbrellas offer very little protection from the sun's rays. Trees offer a bit more protection, but are not a perfect shade source since the sun's rays can filter through the leaves. Wide-brimmed hats are the best source of shade available.