A bstract Measurements of the production cross-sections of the Standard Model (SM) Higgs boson ( H ) decaying into a pair of τ -leptons are presented. The measurements use data collected with the ATLAS detector from pp collisions produced at the Large Hadron Collider at a centre-of-mass energy of $$ \sqrt{s} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msqrt> <mml:mi>s</mml:mi> </mml:msqrt> </mml:math> = 13 TeV, corresponding to an integrated luminosity of 139 fb − 1 . Leptonic ( τ → ℓν ℓ ν τ ) and hadronic ( τ → hadrons ν τ ) decays of the τ -lepton are considered. All measurements account for the branching ratio of H → ττ and are performed with a requirement |y H | &lt; 2 . 5, where y H is the true Higgs boson rapidity. The cross-section of the pp → H → ττ process is measured to be 2 . 94 ± $$ 0.21{\left(\mathrm{stat}\right)}_{-0.32}^{+0.37} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mn>0.21</mml:mn> <mml:msubsup> <mml:mfenced> <mml:mtext>stat</mml:mtext> </mml:mfenced> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>0.32</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>+</mml:mo> <mml:mn>0.37</mml:mn> </mml:mrow> </mml:msubsup> </mml:math> (syst) pb, in agreement with the SM prediction of 3 . 17 ± 0 . 09 pb. Inclusive cross-sections are determined separately for the four dominant production modes: 2 . 65 ± $$ 0.41{\left(\mathrm{stat}\right)}_{-0.67}^{+0.91} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mn>0.41</mml:mn> <mml:msubsup> <mml:mfenced> <mml:mtext>stat</mml:mtext> </mml:mfenced> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>0.67</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>+</mml:mo> <mml:mn>0.91</mml:mn> </mml:mrow> </mml:msubsup> </mml:math> (syst) pb for gluon-gluon fusion, 0 . 197 ± $$ 0.028{\left(\mathrm{stat}\right)}_{-0.026}^{+0.032} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mn>0.028</mml:mn> <mml:msubsup> <mml:mfenced> <mml:mtext>stat</mml:mtext> </mml:mfenced> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>0.026</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>+</mml:mo> <mml:mn>0.032</mml:mn> </mml:mrow> </mml:msubsup> </mml:math> (syst) pb for vector-boson fusion, 0 . 115 ± $$ 0.058{\left(\mathrm{stat}\right)}_{-0.040}^{+0.042} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mn>0.058</mml:mn> <mml:msubsup> <mml:mfenced> <mml:mtext>stat</mml:mtext> </mml:mfenced> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>0.040</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>+</mml:mo> <mml:mn>0.042</mml:mn> </mml:mrow> </mml:msubsup> </mml:math> (syst) pb for vector-boson associated production, and 0 . 033 ± $$ 0.031{\left(\mathrm{stat}\right)}_{-0.017}^{+0.022} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mn>0.031</mml:mn> <mml:msubsup> <mml:mfenced> <mml:mtext>stat</mml:mtext> </mml:mfenced> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>0.017</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>+</mml:mo> <mml:mn>0.022</mml:mn> </mml:mrow> </mml:msubsup> </mml:math> (syst) pb for top-quark pair associated production. Measurements in exclusive regions of the phase space, using the simplified template cross-section framework, are also performed. All results are in agreement with the SM predictions.