A method and apparatus for accessing a contention-based uplink random access channel (RACH) in a single carrier frequency division multiple access (SC-FDMA) system are disclosed. A wireless transmit/receive unit (WTRU) randomly selects a RACH subchannel and a signature among a plurality of available RACH subchannels and signatures. The WTRU transmits a preamble using the selected signature via the selected RACH subchannel at a predetermined or computed transmission power. A base station monitors the RACH to detect the preamble and sends an acquisition indicator (AI) to the WTRU when a signature is detected on the RACH. When receiving a positive acknowledgement, the WTRU sends a message part to the base station. If receiving a negative acknowledgement or no response, the WTRU retransmits the preamble.