This paper presents a method of moments (MoM) analysis, obtains the non-uniform current distribution in closed form, and computes the resulted radiated patterns in both near and far zones, of regular hexagonal loop antennas with electrically large perimeter. An oblique incident field in its general form is considered in the formulation of the non-uniform current distributions. In the Galerkin's MoM analysis, the Fourier exponential series is considered as the full-domain basis function series. As a result, the current distributions along the hexagonal loops are expressed analytically in terms of the azimuth angle for various sizes of large loops. Finally, an alternative vector analysis of the electromagnetic (EM) fields radiated from thin hexagonal loop antennas of arbitrary length a is introduced. This method which employs the dyadic Green's function (DGF) in the derivation of the EM radiated fields makes the analysis general, compact and straightforward in both near- and far-zones. The EM radiated fields are expressed in terms of the vector wave eigenfunctions. Not only the exact solution of the EM fields in the near and far zones outside a are derived by use of the spherical Bessel and Hankel functions of the first kind respectively, but also the inner regions between √3a2 and a are characterized by both the spherical Bessel and Hankel functions of the first kind. Validity of the numerical results is discussed and clarified.