A method and apparatus for efficiently allocating resources to a terminal in a random access system are provided. A method for transmitting an abnormal power down report from a Machine to Machine (M2M) device in a wireless communication system may include transmitting a Bandwidth Request (BR) preamble sequence and a first message to a base station, receiving an uplink resource allocation from the base station, transmitting the abnormal power down report using the uplink resource allocation, and starting a first timer for confirmation of the transmitted abnormal power down report, wherein the first message may include an identifier of the M2M device and a BR index for transmitting an abnormal power down report.