Shear stresses τ on a subduction megathrust play an important role in determining the forces available for mountain building adjacent to a subduction zone. In this study, the temperatures and shear stresses on megathrusts in 11 subduction zones around the Pacific rim (Hikurangi, Tonga, Izu-Ogasawara, western Nankai, northeastern Japan, Aleutians, western Alaska, Cascadia, northern Chile, southern Chile) and SE Asia (northern Sumatra) have been determined. The main constraint is that vertical normal stresses beneath the highlands behind the subduction zone are nearly equal to horizontal normal stresses, in the plane of a trench- or arc-normal section. For a typical brittle and ductile megathrust rheology, frictional shear stress τ = ¿ρgz, for depth z, and ductile shear stress τ = A exp (B/RT) at temperature T, where ¿, A, B are rheological parameters treated as constants. Rheological constants common to all the megathrusts (¿crust, ¿mantle, B) are determined by simultaneously solving for the force balance in the overlying wedge and megathrust thermal structure, using a simplex minimization algorithm, taking account of the induced mantle corner flow at depth (65 ¿ 15 km (2σ)) and constant radiogenic heating (0.65 ¿ 0.3 ¿W m-3 (2σ)) throughout the crust. The A constants are solved individually for each subduction zone, assuming that the maximum depth of interplate slip earthquakes marks the brittle-ductile transition. The best fit solution shows two groupings of megathrusts, with most subduction zones having a low mean shear stress in the range 7--15 MPa (¿crust = 0.032 ¿ 0.006, ¿mantle = 0.019 ¿ 0.004) and unable to support elevations >2.5 km. For a typical frictional sliding coefficient ~0.5, the low effective coefficients of friction suggest high pore fluid pressures at ~95% lithostatic pressure. Tonga and northern Chile require higher shear stresses with ¿crust = 0.095 ¿ 0.024, ¿mantle = 0.026 ¿ 0.007, suggesting slightly lower pore fluid pressures, at ~81% lithostatic. Ductile shear in the crust is poorly resolved but in the mantle appears to show a strong power law dependency, with B = 36 ¿ 18 kJ mol-1. Amantle values are sensitive to the precise value of B but are in the range 1--20 kPa. The power law exponent n for mantle flow is poorly constrained but is likely to be large (n > 4). The brittle-ductile transition in the crust occurs at temperatures in the range 370¿C--512¿C, usually close to the base of the crust and in the mantle at much lower temperatures (180¿C--300¿C), possibly reflecting a marked change in pore fluid pressure or quasi ductile and subfrictional properties. In subduction zones where the subducted slab is older than 50 Ma, a significant proportion of the integrated shear force on the megathrust is taken up where it cuts the mantle and temperatures are ≤300¿C. In much younger subduction zones, the stress transmission is confined mainly to the crust. The shear stresses, particularly in the crust, may be kept low by some sort of lubricant such as abundant water-rich trench fill, which lowers the frictional sliding coefficient or effective viscosity and/or raises pore fluid pressure. The unusual high stress subduction zone in northern Chile lacks significant trench fill and may be poorly lubricated, with a mean shear stress ~37 MPa required to support elevations >4 km in the high Andes. However, where the crust is thin in sediment-starved and poorly lubricated subduction zones, such as Tonga, the mean shear stress will still be low. Sediment may lubricate megathrusts accommodating underthrusting of continental crust, such as in the Himalayas or eastern central Andes, which have a low mean shear stress ~15 MPa.