This article investigates the influences of different material distribution types and flow profiles in the cross section on dynamics of cantilevered axially functionally graded (AFG) pipe. Functionally graded material as a designable material, its appliance in structures can enhance the stability of the structure by adequately choosing the material constituents and arranging constituents' distribution. The governing equation of the pipe system is derived based on the Euler–Bernoulli beam theory and numerically solved by the differential quadrature method (DQM). The influences of different volume fraction function and nonuniform flow velocity distribution on the natural frequencies and average critical flow velocities are discussed according to the numerical results. It can be concluded that the enhanced effect of the AFG material is mainly caused by an increment in the amount of stiffer constituent. With the same amount, pure distribution difference in exponential or power function type that brings stiffer fixed end results in slightly higher critical velocity against flutter. Ignoring the nonuniform flow velocity distribution leads to an overestimation of the pipe's stability and the overestimation is even apparent on AFG pipe. Nonuniform velocity distribution affects the stable flow velocity area and appearance of restabilizing phenomena.