A search for new phenomena in final states containing an e+e- or μ+μ- pair, jets, and large missing transverse momentum is presented. This analysis makes use of proton-proton collision data with an integrated luminosity of 36.1fb-1 , collected during 2015 and 2016 at a centre-of-mass energy s=13TeV with the ATLAS detector at the Large Hadron Collider. The search targets the pair production of supersymmetric coloured particles (squarks or gluinos) and their decays into final states containing an e+e- or μ+μ- pair and the lightest neutralino ( χ~10 ) via one of two next-to-lightest neutralino ( χ~20 ) decay mechanisms: χ~20→Zχ~10 , where the Z boson decays leptonically leading to a peak in the dilepton invariant mass distribution around the Z boson mass; and χ~20→ℓ+ℓ-χ~10 with no intermediate ℓ+ℓ- resonance, yielding a kinematic endpoint in the dilepton invariant mass spectrum. The data are found to be consistent with the Standard Model expectation. Results are interpreted using simplified models, and exclude gluinos and squarks with masses as large as 1.85 and 1.3  Te at 95% confidence level, respectively.