Sputnik Planitia on Pluto is a vast plain consisting of a nitrogen ice deposit filling a broad topographic depression, likely an impact basin. The basin displays a broad, raised rim and is surrounded by numerous extensional fracture systems, each with characteristic orientations with respect to the basin center. The nitrogen ice exerts a large mechanical load on the water ice outer shell crust (here also containing the lithosphere). We calculate models of stress and deformation related to this load, varying dimensional, mechanical, and boundary condition properties of the load and Pluto’s lithosphere, in order to constrain the conditions that led to the formation of the observed tectonic and topographic signals. We demonstrate that the tectonic configuration is diagnostic of a particular set of conditions that hold for the Sputnik basin and Pluto, including moderate elastic lithosphere thickness (50 ± 10 km) and a wide load set into a basin that was pan-shaped and shallow (~3 km) at the time of nitrogen deposition initiation. These tectonic systems show the contributions of both flexural (bending) and membrane (stretching) responses of the lithosphere, with the latter dominating in proportion to the importance of spherical geometry effects (i.e., wide loads). Rim topography may also show an influence of primordial annular trans-basin ice shell thickening from the impact process. Analysis of stress-driven cryomagma transport shows that loading stresses can facilitate ascent of cryomagmas in annular zones around the basin, the locations of which overlap the observed distances from Sputnik of several candidate cryovolcanic sites.