Following the proposal by Müller, Berlinger and Tosatti on a possible coherent quantum regime in SrTi03 below 40 K we have performed elastic measurements to look for possible related anomalies in a near-monodomain crystal. The known anomalies related to the 105 K structural transition were well reproduced. In addition, distinct anomalies were observed below 40 K, both in internal friction and in elastic compliance. The anomalies cannot be explained by phonon interaction with the soft TO mode. A different kind of excitation seems to be required. The features found bear some qualitative resemblance to what is observed in the superfluid phase of4He. © 1992 IOP Publishing Ltd.