Abstract: This paper presents that parameter-control inverse problems for parabolic-type equation and for Poisson equation can be solved respectively by Pulse pectrum Technique (PST) and BEM-optimization method. The solution procedures are formulated and numerical algorithms are given in the paper. The two algorithms have been applied respectively to invert the permeability coefficient of Xinanjiang dam foundation before and after being sthengthened by grouting. Numerical results show that PST and BEM-optimization method are valid for solving parameter-control inverse problems and can be applied to invert the permeability coeihcient of dams and their foundations. The advantages of the two methods are that they need much less additional informations and much less drilling and sampling work,so as to save much investment.