Conventional lithography techniques have been losing their ability to easily support continuous shrinking of feature sizes, especially when the pattern half-pitch is <60 nm. EUV lithography is one of the leading contenders to replace these conventional techniques. Because the EUV mask structure is many times thicker than the illumination wavelength, scalar Fraunhofer diffraction calculations cannot describe the scattering of light from the EUV masks with enough accuracy. In this paper, we present a rigorous 3-D electromagnetic field simulator for EUV masks. The simulator is based on a 3-D waveguide method developed to calculate the characteristics of the light scattered from nonplanar EUV masks. A typical EUV mask contains as many as 80 reflective layers in addition to the absorbing layers, and we have developed a fast method to calculate the scattering matrix of the reflective layers. Also, based on the existing numerical techniques, we can describe the light scattering in the absorbing layers with complex index of refraction. The simulator has been recently modified to handle oblique illumination conditions, and this is the focus of our paper. Aerial images are calculated in the image plane of a typical EUV stepper, and a threshold resist model is used to predict the printed pattern size. We will first compare our work with published results on dense and isolated lines. Then, we will describe the results of our calculations for two-dimensional patterns (e.g., contacts and islands) under oblique illumination. The typical simulation time is less than 10 hours on a desktop workstation for two-dimensional patterns.