In a waveform data processing apparatus, a transfer section reads out waveform data of multiple tracks stored in a first storage device in data units, and transfers the read waveform data to a second storage device having an access speed higher than an access speed of the first storage device. A reproduction section reads out the waveform data of the tracks from the second storage device for every sampling period, and which reproduces an audio signal according to the read waveform data. A control section replaces old waveform data which has been read from the second storage device by new waveform data which is read from the first storage device, whereby the audio signals of the tracks are continuously reproduced. The control section controls the transfer section to transfer, from the first storage device to track regions provided in the second storage device for respective tracks, pieces of the waveform data corresponding to the respective track regions, in an order of the tracks having a smaller number samples of non-reproduced waveform data or in an order of the tracks having a smaller number units of non-reproduced waveform data.