A method for S-NSSAI handling of a 5GS capable UE supporting session continuity between 3GPP and non-3GPP interworking is proposed. The UE maintains a PDN connection/PDU session. The UE performs interworking among S1 mode, N1 mode (including 3GPP and non-3GPP access), and ePDG. The UE associates the existing S-NSSAI with the new PDN connection/PDU session after interworking, no matter whether the S-NSSAI is provided by the network or not. The UE can update the S-NSSAI upon receipt of new value from the network. When interwork to N1 mode, the UE applies the S-NSSAI.