Traditional mesh-based methods in eigen analysis of waveguide meet two big challengers.One comes from the mesh generation

which is a big difficulty especially in complex geometry.The other originates from the local linear approximation

whose approximation accuracy is poor.So radial basis function method was introduced in this paper

which is a kind of meshless methods with collocation type.Ideas on how to solve eigenvalue problems and detailed implementation procedure were presented with corresponding discrete equations.Comparing to finite element method in the analyzing rectangular

round and L-shaped waveguide

the method suggested in this paper can be realized with low computation and high precision.In addition

the radial basis function method can be implemented more convenient and also can be extended into high dimension problems easily.