The largest volcanic constructs on Earth are the seismically imaged seaward dipping reflector (SDR) units found offshore of many rifted continental margins, including most that border the Atlantic Ocean. Whether their formation requires large magnitude (i.e. 10 s of km) of normal fault slip or results from the deflection of the lithosphere by the weight of volcanic flows is controversial. Though there is evidence for faulting associated with some SDRs, this paper considers the range of structures that can be produced by magmatic and volcanic loading alone. To do this an idealized mechanical model for the construction of rift-related volcanic flow structures is developed. Dikes open as plates move away from the center of a model rift and volcanic flows fill the depression produced by the load caused by dike solidification. The thin elastic plate flexure approximation allows a closed form description of the shape of both the contacts between flows and between the flows and underlying dikes. The model depends on two independent parameters: the flexure parameter, alpha, and the maximum isostatically supported extrusive layer thickness, w(0). For reasonable values of these parameters the model reproduces the observed down dip thickening of flows and the range of reflector dip angles. A numerical scheme using the analytic results allows simulation of the effect of temporal changes in the locus of magmatic spreading as well as changes in the amount of volcanic infill. Either jumps in the location of the center of diking or periods with no volcanism result in separate units or "packages" of model SDRs, in which the flow-dike contact dips landward, consistent with observations previously attributed only to listric normal fault offset. When jumps in the spreading center are small (i.e. less than a) they result in thicker, narrower volcanic units on one side of a rift compared to those on the other side. This is similar to the asymmetric distributions of volcanic packages seen across some conjugate margins. (C) 2017 Elsevier B.V. All rights reserved.