The topography of rifts on icy bodies can be used to probe their internal properties. Uplifted and curved rift flanks occur when the elastic thickness (te) of the crust is low, indicative of high heat flow out of the body. Stereo topography of Pluto shows no evidence of rift-flank uplift associated with large extensional graben to the west of Sputnik Planitia. Modeling the amount of topographic deflection expected from varying elastic thicknesses yields a conservative lower bound on te of 8 km at the time of deformation; the maximum implied heat flux since graben formation is 66–85 mWm−2. This upper bound is consistent with the predicted paleo-heat fluxes from radioactive decay (~6 mWm−2), but likely only marginally consistent with nearby apparently viscously-relaxed impact craters. Additionally, we also analyze the shear stresses on these faults and find that Pluto's faults only need to support low stresses in the range of 100–300 kPa to explain their dimensions. •Extensional graben on Pluto's surface show little to no signals of flexure.•This sets a lower limit of 8 km for the elastic layer of Pluto's icy crust.•An upper bound of 85 mWm−2 on the surface heat flux is also set.•This upper bound limits explanations for surface features via high heat flux processes.