jats:pWe consider peeling of an elastic sheet away from an elastic substrate through propagation of a fluid-filled crack along the interface between the two. The peeling is driven by a bending moment applied to the sheet and is resisted by viscous flow towards the crack tip and by the toughness of any bonding between the sheet and the substrate. Travelling-wave solutions are determined using lubrication theory coupled to the full equations of elasticity and fracture. The propagation speed jats:inline-formulajats:alternatives<jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="gif" xlink:type="simple" xlink:href="S002211201900185X_inline1" />jats:tex-math$v$</jats:tex-math></jats:alternatives></jats:inline-formula> scales like jats:inline-formulajats:alternatives<jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="gif" xlink:type="simple" xlink:href="S002211201900185X_inline2" />jats:tex-math$M3/𝜇E¯2d5=Bd𝜅3/144𝜇$</jats:tex-math></jats:alternatives></jats:inline-formula>, where jats:inline-formulajats:alternatives<jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="gif" xlink:type="simple" xlink:href="S002211201900185X_inline3" />jats:tex-math$d$</jats:tex-math></jats:alternatives></jats:inline-formula> is the sheet’s thickness, jats:inline-formulajats:alternatives<jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="gif" xlink:type="simple" xlink:href="S002211201900185X_inline4" />jats:tex-math$B=E¯d3/12$</jats:tex-math></jats:alternatives></jats:inline-formula> its stiffness, jats:inline-formulajats:alternatives<jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="gif" xlink:type="simple" xlink:href="S002211201900185X_inline5" />jats:tex-math$E¯=E/(1-𝜈2)$</jats:tex-math></jats:alternatives></jats:inline-formula> its plane-strain modulus, jats:inline-formulajats:alternatives<jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="gif" xlink:type="simple" xlink:href="S002211201900185X_inline6" />jats:tex-math$𝜇$</jats:tex-math></jats:alternatives></jats:inline-formula> the fluid viscosity, jats:inline-formulajats:alternatives<jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="gif" xlink:type="simple" xlink:href="S002211201900185X_inline7" />jats:tex-math$M$</jats:tex-math></jats:alternatives></jats:inline-formula> the applied bending moment and jats:inline-formulajats:alternatives<jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="gif" xlink:type="simple" xlink:href="S002211201900185X_inline8" />jats:tex-math$𝜅=M/B$</jats:tex-math></jats:alternatives></jats:inline-formula> the sheet’s curvature due to bending; and the prefactor depends on the dimensionless toughness. If the toughness is small then there is a region of dry shear failure ahead of the fluid-filled region. The expressions for the propagation speed have been used to derive new similarity solutions for the spread of an axisymmetric fluid-filled blister in a variety of regimes: constant-flux injection resisted by elastohydrodynamics in the tip leads to spread proportional to jats:inline-formulajats:alternatives<jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="gif" xlink:type="simple" xlink:href="S002211201900185X_inline9" />jats:tex-math$t4/13$</jats:tex-math></jats:alternatives></jats:inline-formula>, jats:inline-formulajats:alternatives<jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="gif" xlink:type="simple" xlink:href="S002211201900185X_inline10" />jats:tex-math$t4/17$</jats:tex-math></jats:alternatives></jats:inline-formula> and jats:inline-formulajats:alternatives<jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="gif" xlink:type="simple" xlink:href="S002211201900185X_inline11" />jats:tex-math$t7/19$</jats:tex-math></jats:alternatives></jats:inline-formula> for peeling-by-bending, gravitational spreading and peeling-by-pulling, respectively.</jats:p>