A method for updating Short Message service, SMS, over Non Access Stratum, NAS, support capability of a User Equipment, UE, performed by an Access and Mobility Management Function, AMF, comprising: determining that SMS over NAS support capability update needs to be triggered; updating SMS over NAS support capability of the UE; the determining that the SMS over NAS support capability update needs to be triggered comprises: determining that the SMS over NAS support capability update needs to be triggered through a change in the SMS over NAS support capability triggered by a network due to a change in operator configuration; or determining that the SMS over NAS support capability update needs to be triggered through a change in subscription data obtained from a User Data Management, UDM, function; or determining that the SMS over NAS support capability update needs to be triggered through a change of policy information of a user; or determining that the SMS over NAS support capability update needs to be triggered through a change in information is obtained through a Short Message Service Function, SMSF; or determining that the SMS over NAS support capability update needs to be triggered through a change in the SMS over NAS support capability triggered by a network due to that the LTE performs a deregistration procedure of which an access type is non-3rd generation partnership project, non-3GPP. determining that SMS over NAS support capability update needs to be triggered; updating SMS over NAS support capability of the UE; the determining that the SMS over NAS support capability update needs to be triggered comprises: determining that the SMS over NAS support capability update needs to be triggered through a change in the SMS over NAS support capability triggered by a network due to a change in operator configuration; or determining that the SMS over NAS support capability update needs to be triggered through a change in subscription data obtained from a User Data Management, UDM, function; or determining that the SMS over NAS support capability update needs to be triggered through a change of policy information of a user; or determining that the SMS over NAS support capability update needs to be triggered through a change in information is obtained through a Short Message Service Function, SMSF; or determining that the SMS over NAS support capability update needs to be triggered through a change in the SMS over NAS support capability triggered by a network due to that the LTE performs a deregistration procedure of which an access type is non-3rd generation partnership project, non-3GPP. determining that the SMS over NAS support capability update needs to be triggered through a change in the SMS over NAS support capability triggered by a network due to a change in operator configuration; or determining that the SMS over NAS support capability update needs to be triggered through a change in subscription data obtained from a User Data Management, UDM, function; or determining that the SMS over NAS support capability update needs to be triggered through a change of policy information of a user; or determining that the SMS over NAS support capability update needs to be triggered through a change in information is obtained through a Short Message Service Function, SMSF; or determining that the SMS over NAS support capability update needs to be triggered through a change in the SMS over NAS support capability triggered by a network due to that the LTE performs a deregistration procedure of which an access type is non-3rd generation partnership project, non-3GPP.