Shadow has been increasingly a kind of significant aid information for object extraction and scene interpretation in synthetic aperture radar images, which makes SAR shadow detection an important issue. In this paper, we propose a feed‐forward framework integrating saliency and geometry discrimination for shadow detection in SAR images. We firstly develop a global contrast based shadow saliency model to extract suspected shadows. Considering that such suspected regions mostly contain some non‐shadow areas, a discrimination strategy based on geometric relationships between objects and shadows is designed to remove falsely detected areas. Then the remaining regions become the final shadow detection results. Several experiments are carried out on images from two real datasets, Moving and Stationary Target Acquisition Recognition and MiniSAR, to evaluate the performance of our method. From the perspectives of three commonly used metrics, the proposed algorithm comprehensively outperforms two other classic methods, presenting reliable shadow detection ability. Moreover, the detection results of the two classic methods are significantly enhanced in controlling false alarms after the discrimination module is introduced. The results demonstrate that our algorithm is practically applicable to shadow detection in SAR images, and the discrimination strategy can be flexibly extended for related tasks.