Rigorous electromagnetic simulation with TEMPEST is used to examine the use of phase-shifting masks in EUV lithography. The effects of oblique incident illumination and mask patterning by ion-mixing of multilayers are analyzed. Oblique incident illumination causes streamers at absorber edges and causes position shifting in aerial images. The diffraction waves between ion-mixed and pristine multilayers are observed. The phase-shifting caused by stepped substrates is simulated and images show that it succeeds in creation of phase-shifting effects. The diffraction process at the phase boundary is also analyzed. As an example of EUV phase-shifting masks, a coma pattern and probe based aberration monitor is simulated and aerial images are formed under different levels of coma aberration. The probe signal rises quickly as coma increases as designed.