Accurate classification and localization of anatomical structures in images is a precursor for fully automatic image-based diagnosis of placental abnormalities. For placental ultrasound images, typically acquired in clinical screening and risk assessment clinics, these structures can have quite indistinct boundaries and low contrast, and image-level interpretation is a challenging and time-consuming task even for experienced clinicians. In this paper, we propose an automatic classification model for anatomy recognition in placental ultrasound images. We employ deep residual networks to effectively learn discriminative features in an end-to-end fashion. Experimental results on a large placental ultra-sound image database (10,808 distinct 2D image patches from 60 placental ultrasound volumes) demonstrate that the proposed network architecture design achieves a very high recognition accuracy (0.086 top-1 error rate) and provides good localization for complex anatomical structures around the placenta in a weakly supervised fashion. To our knowledge this is the first successful demonstration of multi-structure detection in placental ultrasound images.