Simultaneous prediction of wrist and hand motions is essential for the natural interaction with hand prostheses. In this paper, we propose a novel multi-out Gaussian process (MOGP) model and a multi-task deep learning (MTDL) algorithm to achieve simultaneous prediction of wrist rotation (pronation/supination) and finger gestures for transradial amputees via a wearable ultrasound array. We target six finger gestures with concurrent wrist rotation in four transradial amputees. Results show that MOGP outperforms previously reported subclass discriminant analysis for both predictions of discrete finger gestures and continuous wrist rotation. Moreover, we find that MTDL has the potential to improve the accuracy of finger gesture prediction compared to MOGP and classification-specific deep learning, albeit at the expense of reducing the accuracy of wrist rotation prediction. Extended comparative analysis shows the superiority of ultrasound over surface electromyography. This paper prioritizes exploring the performance of wearable ultrasound on the simultaneous prediction of wrist and hand motions for transradial amputees, demonstrating the potential of ultrasound in future prosthetic control. Our ultrasound-based adaptive prosthetic control dataset (Ultra-Pro) will be released to promote the development of the prosthetic community.