The low-frequency mechanical spectra of lanthanum cobaltite based mixed conducting oxides have been measured using a computer-controlled inverted torsion pendulum. The results indicate that the internal friction spectra and shear modulus depend on the Sr doping contents (x). For undoped samples, no internal friction peak is observed. However, for La0.8Sr0.2CoO3‒δ, three internal friction peaks (P2, P3 and P4) are observed. In addition to these peaks, two more peaks (P0 and P1) are observed in La0.6Sr0.4CoO3‒δ. The P0 and P1 peaks show characteristics of a phase transition, while the P2, P3 and P4 peaks are of relaxation-type. Our analysis suggests that the P0 peak is due to a phase separation and the P1 peak is related to the ferromagnetic–paramagnetic phase transition. The P2, P3 and P4 peaks are associated with the motion of domain walls. The formation of this kind of domain structure is a consequence of a transformation from the paraelastic cubic phase to the ferroelastic rhombohedral phase. With partial substitution of Fe for Co, only one peak is observed, which is discussed as a result of different microstructure.