This paper proposes a parametric analytical source model for overall representation of the physical distribution property of off-axis illumination sources in lithographic tools. A Sigmoid function is adopted as a kernel function to construct the analytical model for the multiple mainstream off-axis sources. Corrected parametrical terms are subsequently presented for characterization of different physical distortions and deviations of real illumination sources. The corrected parametrical terms can be decomposed into Fourier series which have the special physical meaning of respectively indicating different distortion types including shift of the center, tilt, ellipticity, etc. The proposed analytical model provides both simulation condition and theoretical basis for the resolution enhancement technique and the related research fields, thus has important applications.