Although there has been extensive research and many applications of the finite-difference time-domain (FDTD) method to electromagnetic scattering problems, little has been reported toward applying this method to model antenna radiation. Here the FDTD method is used to model and predict the radiation patterns of wire and aperture antennas of three basic configurations. A critical step in each is the modeling of the feed. Alternate suggestions are made and some are implemented. The first antenna is a quarter-wavelength monopole and the second is a waveguide aperture antenna. In both cases the antenna is mounted on ground planes, either perfectly conducting or of composite material. The results obtained using the FDTD technique are compared with results obtained using the geometrical theory of diffraction (GTD) and measurements. The third configuration of interest is a pyramidal horn antenna. To model the flared parts of the horn, a staircase approximation was applied to the antenna surface. The computed radiation patterns compared well with measurements.