The transfer matrices of the axial, flexible and torsional modes of fluidconveying elbow pipe are deduced considering fluidstructure interaction between pipe and fluid. Calculate the modal frequency and shape of a “U” shape pipe with Transfer Matrix Method and ANSYS software respectively. The results indicate that Transfer Matrix Method is an effective way to analyze fluidconveying pipe. The effect of fluidstructure interaction can not be ignored which will depress the modal frequency of the pipe.