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I presume that you refer to X or gamma radiation, rather than alpha or beta because the latter two types of radiation can easily be stopped by thin layer of light materials.
The most important interaction process when X or gamma rays enter into a material is [photoelectric effect (光電效應)], in which the X or gamma photon causes ionizing to atoms of the absorption material, with the absorption of the photon resulted in an emission of a free electron.
From quantum theory, photoelectric absorption is proportional to the cube of the atomic number of the absorption material. That is to say, materials of heavy elements (high atomic number) can absorb X or gamma rays far better than materials of light elements.
Therefore, lead is not the only material that is effective in shielding X or gamma rays. Other materials with high atomic number, like platinum, bismuth, gold, iridium etc can also absorb X or gamma rays effectively. Lead is commonly used because of its large abundance and low cost. In fact, depleted uranium (uranium with most of its radioactivity removed), which is the heaviest natural occurring element, is the best material is radiation shielding. But due to its high cost as compared with lead, it is only used in some special situation like that in military purpose.
You may also wish to look at my previous answer given to a similar question,
http://hk.knowledge.yahoo.com/question/question?qid=7008112201436