An antiferro ordering of an electric hexadecapole moment is discussed as a promising candidate for the long standing mystery of the hidden order phase in URu2Si2. Based on localized f-electron picture, we discuss the rationale of the selected multipole and the consequences of the antiferro hexadecapole order of xy(x2 - y2) symmetry. The mean-field solutions and the collective excitations from them explain reasonably significant experimental observations: the strong anisotropy in the magnetic susceptibility, characteristic behavior of pressure versus magnetic field or temperature phase diagrams, disappearance of inelastic neutron-scattering intensity out of the hidden order phase, and insensitiveness of the NQR frequency at Ru-sites upon ordering. A consistency with the strong anisotropy in the magnetic responses excludes all the multipoles in two-dimensional representations, such as (Oyz; Ozx). The expected azimuthal angle dependences of the resonant X-ray scattering amplitude are given. The (x2 - y2)-type antiferro quadrupole should be induced by an in-plane magnetic field along , which is reflected in the thermal expansion and the elastic constant of the transverse (c11 - c12)=2 mode. The (x2 - y2)-type [(xy)-type] antiferro quadrupole is also induced by applying the uniaxial stress along  direction [ direction]. A detection of these induced antiferro quadrupoles under the in-plane magnetic field or the uniaxial stress using the resonant X-ray scattering provides a direct redundant test for the proposed order parameter.