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With the scales of systems becoming larger and larger gradually, it is necessary to research brittleness of complex system. The lingual description and mathematic definition of brittleness are given separately. On the basis of the definition of brittleness source and brittleness receiver, the brittleness relevance is presented and three regulations are given due to it. Meanwhile, the method of establishing brittleness potential function is given. Taking SARS, which happened in China in spring of 2003, as example to analyze brittleness of complex system. The direct analysis of SARS is given by using cusp catastrophe model. On the basis of data from Ministry of Health P.R. China from April to May in 2003, take Peking as example to match polynomial. The brittleness analysis of SARS is given through the mat ching polynomial.