The present invention relates to a wireless access system which supports machine-type communication (MTC), and more particularly, to various methods for efficiently transmitting, by an MTC terminal, uplink control information (UCI) and/or user data, and to apparatuses supporting same. A method for transmitting an uplink by an MTC terminal which supports machine-type communication (MTC) in a wireless access system, according to one embodiment of the present invention, may comprise the steps of: determining whether an overlap exists between a plurality of physical uplink control channels (PUCCHs) for transmitting uplink control information (UCI) and a plurality of physical uplink shared channels (PUSCHs) for transmitting user data; multiplexing UCI in at least one subframe on an overlapping PUSCH when the plurality of PUCCHs and the plurality of PUSCHs overlap in the at least one subframe; and transmitting the PUSCH on which the UCI has been multiplexed in the at least one subframe.