This paper proposes a novel extended object tracking (EOT) approach with embedded classification. Traditionally, for extended objects, only tracking is addressed without considering classification. This has serious defects: On the one hand, some practical EOT problems require classification as an embedded subproblem; on the other hand, with the assistance of classification, the tracking performance can be improved. Therefore, we propose a systematic EOT method with embedded classification, which is desired to satisfy the practical demands and also enjoys superior tracking performance. Specifically, we first formulate the EOT problem with embedded classification by kinematic models and attribute models. Then, we explore a random-matrix-based, multiple model EOT method with embedded classification. Two strategies are creatively provided in which soft classification and hard classification are embedded, respectively. Especially for the EOT with hard classification, a sequential probability ratio-test-based classification scheme is explored due to its nice properties and adaptability to our problem. In both methods, classification assist tracking is used. The simulation results demonstrate the superiority of the proposed EOT method with embedded classification, which can not only satisfy the practical requirements for classification but can also improve the tracking performance by utilizing the assistant of classification.