Abstract: Ambiguity Function (AF) can describe measuring accuracy, clutter suppression characteristic and signal resolution characteristic determined by radar signal. AF of conventional radar based on time delay and Doppler frequency of radar signal is not appropriate for resolution analysis of SAR. This paper deduces Generalized Ambiguity Function (GAF) of Frequency Modulated Continuous Wave (FMCW) SAR based on GAF theory of conventional SAR. AF of two new kinds of typical array FMCW SAR system: Forward-Looking (FL) array FMCW SAR and Downward-Looking (DL) array FMCW SAR are analyzed further. GAF of FL array FMCW SAR is defined according to AF of conventional FMCW SAR. According to the feature of DL array SAR, and inspired by AF of formation flying satellites SAR whose structure is similar to that of DL array SAR, GAF of DL array FMCW SAR is modeled. Ambiguity factors are combined to analyze resolution characteristic of the two kinds of system. The analyzing approach based on AF for array FMCW SAR proposed in this paper can provide valuable reference for comprehension of parameter choice and system design of FL and DL array SAR.