Aerial robots such as drones have been leveraged to perform bridge inspections. Inspection images with both recognizable structural elements and apparent surface defects can be collected by onboard cameras to provide valuable information for the condition assessment. This article aims to determine a suitable deep neural network (DNN) for parsing multiclass bridge elements in inspection images. An extensive set of quantitative evaluations along with qualitative examples show that High-Resolution Net (HRNet) possesses the desired ability. With data augmentation and a training sample of 130 images, a pre-trained HRNet is efficiently transferred to the task of structural element parsing and has achieved a 92.67% mean F1-score and 86.33% mean IoU.