Giant earthquake (moment magnitude M-w >= 8.5) forecasts for subduction zones have been empirically related to both tectonic stresses and geometrical irregularities along the subduction interface. Both of these controls have been suggested as able to tune the ability of rupture to propagate laterally and, in turn, exert an important control on giant earthquake generation. Here we test these hypotheses, and their combined influence, by compiling a dataset of trench fill thickness (a proxy for smoothing of subducting plate relief by sediment input into the subduction channel) and upper plate strain (a proxy for the tectonic stresses applied to the subduction interface) for 44 segments of the global subduction network. We statistically compare relationships between upper plate strain, trench sediment thickness and maximal earthquake magnitude. We find that the combination of both large trench fill (>= 1 km) and neutral upper plate strain explains spatial patterns of giant earthquake occurrence to a statistically significant degree. In fact, the concert of these two factors is more highly correlated with giant earthquake occurrence than either factor on its own. Less frequent giant earthquakes of lower magnitude are also possible at subduction zones with thinner trench fill and compressive upper plate strain. Extensional upper plate strain and trench fill < 0.5 km appear to be unfavorable conditions, as giant earthquakes have not been observed in these geodynamical environments during the last 111 years. Citation: Heuret, A., C. P. Conrad, F. Funiciello, S. Lallemand, and L. Sandri (2012), Relation between subduction megathrust earthquakes, trench sediment thickness and upper plate strain, Geophys. Res. Lett., 39, L05304, doi: 10.1029/2011GL050712.