Embodiments of the present invention disclose a communication method, an access network device, and a core network device. The method includes: sending, by a source access network device, to a core network device a handover message for a handover of one or more sessions of a terminal device from the source access network device to a target access network device, wherein the handover message comprises information about the target access network device and identifier information of the one or more sessions; and sending, by the core network device, a response message of the handover message to the source access network device, wherein the response message of the handover message comprises indication information indicating a reason that a session of the one or more sessions is not accepted, wherein the reason is associated with a slice corresponding to the session.