The vibration of post - buckl ed fluid - conveying pipe made of functionally graded material is analyzed . The pipe material properties are assumed to be graded in the thickness dire ction according to power - law distribution. A n exact solution is obtained for the post - buckling deformation of the fluid - conveying functionally graded pipe with various boundary conditions. T he linear vibration problem is solved around the first buckled con figuration and t he natural frequencies of the three lowest vibration modes are obtained. The influences of power - law exponent, initial tension, fluid density and fluid velocity on the static deflection and free vibration frequencies are studied.