Unilateral problems is a kind of important partial differential problems. It can be solved by treating it as a complementary problem. As the complementary conditions lie in the boundary of the region,it is suitable for BEM. This paper is based on the switching algorithm,which is first used by J. M. Aitchison for the Signorini Problems of Laplace operator,then extends it to the elliptic operator,and conjunct it with the BEM. At last the detail of the algorithm is given. The new algorithm is easy to be implied effectively and quickly. It only needs the minimal change of the BEM programming. The numerical tests show the algorithm is effective and conventional.
