A wheel assembly position identifying apparatus includes transmitters, each of which is provided in one of wheel assemblies, and a receiver, which is provided in a body of a vehicle. Each transmitter includes a transmission section, an acceleration sensor, and a transmission-side control section. The receiver includes a reception section, which is configured to receive the signals, and a reception-side control section, which is configured to execute a first identifying process and a second identifying process. In the first identifying process, the positions of the wheel assemblies, in which the corresponding transmitters are provided, are identified based on variations of the rotational positions of the wheel assemblies at the time when the constant position signals are received. In the second identifying process, the positions of the wheel assemblies, in which the corresponding transmitters are provided, are identified based on the received signal strength indications (RSSIs).