In this thesis, firstly, Radial Basis Functions (RBF) are introduced. Then, using RBF, Traditional Radial Basis Function (TRB) Interpolation and Osculatory Radial
Basis Fuctions (ORBF) Interpolations are given and compared on some different test functions. Application of these interpolation techniques with Dual Reciprocity
Boundary Element Method (DRBEM) is given separately for Poisson's equations of the forms \/^2u=b(x,y), \/^2u=b(x,y,u) and \/^2u=b(x,y,u,u_x,u_y). The
DRBEM itself is explained in details and applications are given especially for solving magnetohydrodynamic channel flow problems which are nonlinear Poisson's
type equations. The results agree well with the exact solution and it is found that osculatory interpolation gives better results.

Keywords : Interpolation, Radial basis functions, Poisson's equation, Dual reciprocity boundary element method.