A waveform reproduction apparatus and process for carrying out waveform reproduction without delays. Waveform data expressing first and latter half portions of a musical tone waveform are stored on a storage device. In response to a tone generation start indicator, waveform data that express first half portions corresponding to the tone generation start indicator are successively read out and corresponding musical tone waveforms are formed. Following this, the waveform data that express latter half portions corresponding to the tone generation start indicator are successively read out and corresponding musical tone waveforms are formed. After the first half portions are successively read out and corresponding musical tone waveforms are formed, if the read-out of the waveform data that express the latter half portions corresponding to the tone generation start indicator is not completed in time, the formation of the musical tone waveforms is based on a specified segment set in the first half portion of the waveform data.