The anitferrodistortive phase transitions in uniaxially -stressed SrTiO3 were investigated by means of elastic and inelastic neutron scattering. From elastic intensity measurements at the (32,12,52) and (12,32,52) cubic R points, the P-T phase diagram was obtained in agreement with an earlier EPR determination. In the cubic phase, the effect of stress is to split the triply degenerate R25 mode into a singlet (A) mode, corresponding to octahedra rotations around the stress axis, and a doublet (E) mode. Condensation of the A component leads to the stress-induced trigonal phase. The dynamic responses from each of the two components were measured separately in the stressed cubic phase, by means of inelastic scattering at the above-mentioned R points. The experimental line shapes are analyzed in terms of the usual damped oscillator central-peak model. The resulting best-fit values for the A- and E-mode quasiharmonic frequencies 2 and central-peak strengths 2 are obtained as a function of temperature and compared to the corresponding zero-stress values. In the mean-field range and in the presence of  stress the frequencies agree with the prediction of the Landau model and known stress coupling constants. At zero stress, the central-peak behavior is found to be sample dependent. For T>Tc, this latter result is discussed in the light of recent theories on the coupling of soft modes with slowly relaxing defects. © 1978 The American Physical Society.