In VHF and UHF bands, antenna patterns for short range airborne communications are required to be omni-directional. Contributions from reflections and diffractions from the airframe usually distort the primary radiation patterns of antennas mounted on airframes. Moreover, these diffractions and reflections become increasingly important as the frequency of operation increases. Therefore, for this type of application, an antenna performance simulated without the airframe is not an accurate representation. In this study, an accurate and versatile finite element method (FEM) based on the discretization of Helmholtz's equation has been developed to analyze VHF and UHF antennas mounted on helicopter airframes, parts of which may include composite material and anisotropies. The FEM code was implemented with linear edge-based tetrahedral elements and first/second-order Absorbing Boundary Conditions. Possible material anisotropies in the computational domain are accounted for by using a permittivity and a permeability tensor. Radiation characteristics are predicted for absolute gain, spatial field distribution, input impedance and return loss, and then compared with measurements for verification.