Based on the generalized Huygens-Fresnel diffraction integral and the unified theory of coherence and polarization, propagation properties of partially coherent electromagnetic square flat-topped pulsed beams with amplitude and phase modulations in free space are analyzed. The analytical expressions for the cross-spectral density matrix of partially coherent electromagnetic square flat-topped pulsed beams with amplitude and phase modulations in free space are derived, and the numerical calculations are also given. It is shown that the spectral intensity distribution of partially coherent electromagnetic square flat-topped pulsed beams is influenced by size of the modulation zone, the depth of amplitude and phase modulations, the coherence length and temporal coherence length of the beams, and transmission distance.