Raven's Progressive Matrices (RPM), one of the standard intelligence tests in human psychology, has recently emerged as a powerful tool for studying abstract visual reasoning (AVR) abilities in machines. Although existing computational models for RPM problems achieve good performance, they require a large number of labeled training examples for supervised learning. In contrast, humans can efficiently solve unlabeled RPM problems after learning from only a few example questions. Here, we develop a semi-supervised learning (SSL) method, called RuleMatch, to train deep models with a small number of labeled RPM questions along with other unlabeled questions. Moreover, instead of using pixel-level augmentation in object perception tasks, we exploit the nature of RPM problems and augment the data at the level of abstract rules. Specifically, we disrupt the possible rules contained among context images in an RPM question and force the two augmented variants of the same unlabeled sample to obey the same abstract rule and predict a common pseudo label for training. Extensive experiments show that the proposed RuleMatch achieves state-of-the-art performance on two popular RAVEN datasets. Our work makes an important stride in aligning abstract analogical visual reasoning abilities in machines and humans. Our Code is at https://github.com/ZjjConan/AVR-RuleMatch.