This presentation discusses a numerical method for determining resonance frequencies for waveguide problems in a two dimensional infinite strip with homogeneous Neumann boundary conditions on the sides of the strip.We use the BIEM(Boundary Integral Equation Method)with Green's function for the waveguide problems to this end.It is known that there exist frequencies near which the behavior of the solution changes suddenly.These frequencies can be classified into two types.One is the cut-off frequency(also called Wood's anomaly in mathematical communities)at which Green's function diverges.The location(i.e.,the value of the frequency)of the cut-off frequency is known.The other type of anomalies is the resonance anomaly which is related to the existence of resonance frequencies.