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Simple Summary: Breast cancer is one of the most common cancers among women globally. Early and accurate screening of breast tumours can improve survival. Ultrasound elastography is a non-invasive and non-ionizing imaging approach to characterize lesions for breast cancer screening, while machine learning techniques could improve the accuracy and reliability of computer-aided diagnosis. This review focuses on the state-of-the-art development and application of the machine learning model in breast tumour classification. Ultrasound elastography can quantify stiffness distribution of tissue lesions and complements conventional B-mode ultrasound for breast cancer screening. Recently, the development of computer-aided diagnosis has improved the reliability of the system, whilst the inception of machine learning, such as deep learning, has further extended its power by facilitating automated segmentation and tumour classification. The objective of this review was to summarize application of the machine learning model to ultrasound elastography systems for breast tumour classification. Review databases included PubMed, Web of Science, CINAHL, and EMBASE. Thirteen (n = 13) articles were eligible for review. Shear-wave elastography was investigated in six articles, whereas seven studies focused on strain elastography (5 freehand and 2 Acoustic Radiation Force). Traditional computer vision workflow was common in strain elastography with separated image segmentation, feature extraction, and classifier functions using different algorithm-based methods, neural networks or support vector machines (SVM). Shear-wave elastography often adopts the deep learning model, convolutional neural network (CNN), that integrates functional tasks. All of the reviewed articles achieved sensitivity ≥80%, while only half of them attained acceptable specificity ≥95%. Deep learning models did not necessarily perform better than traditional computer vision workflow. Nevertheless, there were inconsistencies and insufficiencies in reporting and calculation, such as the testing dataset, cross-validation, and methods to avoid overfitting. Most of the studies did not report loss or hyperparameters. Future studies may consider using the deep network with an attention layer to locate the targeted object automatically and online training to facilitate efficient re-training for sequential data. [ABSTRACT FROM AUTHOR]