Based on a sample of 1.31×109 J/ψ events collected with the BESIII detector at the BEPCII collider, Dalitz plot analyses of selected 79,625 η→π+π-π0 events, 33,908 η→π0π0π0 events, and 1,888 η′→π0π0π0 events are performed. The measured matrix elements of η→π+π-π0 are in reasonable agreement with previous measurements. The Dalitz plot slope parameters of η→π0π0π0 and η′→π0π0π0 are determined to be -0.055±0.014±0.004 and -0.640±0.046±0.047, respectively, where the first uncertainties are statistical and the second systematic. Both values are consistent with previous measurements, while the precision of the latter one is improved by a factor of 3. Final state interactions are found to have an important role in those decays.