Applied mathematics and mechanics have been widely developed in China during the past twenty years. Especially in the development of generalized variational principles, finite deformation, singular perturbation theory, nonhomogenious elasticity, Chinese scientist have made a great impact by evolving new methods and concepts. This survey of the present situation in the area of science is a remarkable contribution to the academic exchange between China and other countries. It contains articles of the leading Chinese scientists in their respective fields.