In this paper, the governing equation for a pipe conveying fluid is modifired by including the influence of the following factors : (1) difference between pressures within and around the pipe ; (2) boundary conditions of fluid and pipe. The solution of the new general basic equation depends on the boundary condition. Application of the new equation to a cantilevered pipe dischanging fluid gives a result closer to the experimental value than the previous theoretical one. The critical speed of the cantilevered pipe aspirating fluid obtained from the new theory is higher than that obtained from the previous theory.