<p>Moment loading is involved in some simulations of beam elements based on the absolute nodal coordinate formulation (ANCF). However, the formulation of the generalized moment vector for three-dimensional Euler-Bernoulli ANCF beam elements has not yet been obtained. Two generalized external moment formulations are proposed for two forms of Euler-Bernoulli ANCF beam elements. For the element that the cross-section coordinate system is defined by three Euler angles, a precise formulation for the generalized moment vector is derived from the relationships between the infinitesimal rotations in the inertial frame and in the cross-section coordinate system in deformed configuration, according to the principle of summation of infinitesimal variations of Euler angles. For the other element with only one Euler angle, an approximate formulation for the generalized moment vector is obtained by replacing the position gradient in the generalized moment vector of the three-dimensional fully parameterized beam elements with three unit vectors. Finally, numerical examples are presented to validate the applicability of the two formulations, and the results are compared with the commercial finite element software. It is shown that both formulations can simulate the imposed concentrated moment at any location of the beam effectively.</p>