Sonomyography (SMG) is the signal we previously termed to describe muscle contraction using real-time muscle thickness changes extracted from ultrasound images. In this paper, we used least squares support vector machine (LS-SVM) and artificial neural networks (ANN) to predict dynamic wrist angles from SMG signals. Synchronized wrist angle and SMG signals from the extensor carpi radialis muscles of five normal subjects were recorded during the process of wrist extension and flexion at rates of 15, 22.5, and 30 cycles/min, respectively. An LS-SVM model together with back-propagation (BP) and radial basis function (RBF) ANN was developed and trained using the data sets collected at the rate of 22.5 cycles/min for each subject. The established LS-SVM and ANN models were then used to predict the wrist angles for the remained data sets obtained at different extension rates. It was found that the wrist angle signals collected at different rates could be accurately predicted by all the three methods, based on the values of root mean square difference (RMSD 0.98), with the performance of the LS-SVM model being significantly better (RMSD 0.99) than those of its counterparts. The results also demonstrated that the models established for the rate of 22.5 cycles/min could be used for the prediction from SMG data sets obtained under other extension rates. It was concluded that the wrist angle could be precisely estimated from the thickness changes of the extensor carpi radialis using LS-SVM or ANN models.