In order to improve the resolution of photolithographic system,hyper numerical aperture is needed.However,analysis of transfer function with Fourier diffraction theory will be inadequate,and shadowing effects must be considered for oblique illumination.Therefore,a new approximation model for alternating phase shift mask considering shadowing effects was proposed in this paper,and shadowing ratio was redefined.Extended Fourier diffraction theory was used,and a relation of function depended on incident angle.Expressions for alternating phase shift mask were given for both space domain and frequency domain.Diffraction efficiencies and interference fields were simulated using approximation model.The results show that diffraction efficiencies and interference fields vary with incident angles and diffraction efficiencies vary with linewidth too.Moreover,diffraction efficiencies are symmetric about the zero incident angle.