Big data, innovative technology, and artificial intelligence (AI) have exerted a profound influence on traditional bureaucracy, creating a new form of algorithmic bureaucracy, the ‘algorithmic cage’ and the ‘algorithmic colleague’ models. Existing literature illustrates algorithms’ highly complex and heterogeneous influence on bureaucracies; however, it does not cover the various forms, patterns, and features of algorithmic bureaucracy. We develop an analytical framework of algorithmic bureaucracy and demonstrate how the four models of algorithmic bureaucracy are derived from the interplay between algorithmic function and application system. This analytical framework provides a further understanding of the algorithmisation of bureaucratic organisation. It extends previous research through its analysis of the role of algorithmic function and its application system in the transition of bureaucracy. We also illustrate the four models of algorithmic bureaucracy through the four cases of AI applications, offering a more balanced and nuanced picture of AI applications in the public administration sector in China than the current dominant study of digital authoritarianism.