Methods and apparatuses for triggering an aperiodic SRS are disclosed. A method comprises receiving a RRC signaling configuring N triggering offsets for each of P aperiodic SRS resource sets, where N is 1 or more, P is 1 or more; receiving a MAC CE to activate one or more triggering offset(s) among all configured triggering offsets for each of M out of the P aperiodic SRS resource sets, where M is 1 to P; receiving a DCI containing a non-zero SRS request field triggering at least one aperiodic SRS resource set, wherein at least one triggering offset of each triggered aperiodic SRS resource set is activated by the MAC CE; and transmitting SRS resources contained in each triggered aperiodic SRS resource set in the first available slot among all candidate slots indicated by the activated triggering offsets for each triggered aperiodic SRS resource set.