A search for Higgs boson pair (di-Higgs) production in events with two 𝑏-jets and two 𝜏-leptons (𝑏𝑏𝜏+ 𝜏−) is presented, using a proton–proton collision data set with an integrated luminosity of 139 fb− 1 collected at√ 𝑠= 13 TeV by the ATLAS experiment at the LHC. DiHiggs produced non-resonantly, or in the decay of a generic narrow-width scalar resonance in the mass range 251 to 1600 GeV is targeted. Events in which one 𝜏-lepton decays leptonically and the other decays hadronically (the 𝜏 lep 𝜏 had decay channel) are considered. Multivariate discriminants are used to extract the signals. No significant excess of events above the expected background is observed in the non-resonant search, therefore upper limits are set on the non-resonant di-Higgs production cross-section. Upper limits are also set on the resonant di-Higgs production cross-section. The search results are then reinterpreted in the framework of Higgs Effective Fields Theory (HEFT), where the nonresonant di-Higgs production is modified by assuming seven HEFT benchmark models. One-dimensional scans are performed on the Higgs boson self-coupling modifier 𝜅 𝜆 and two HEFT coupling parameters associated with the couplings of a Higgs boson pair with two gluons, 𝑐 𝑔𝑔ℎℎ, and with a top quark pair, 𝑐 𝑡𝑡ℎℎ.