A simple two-dimensional inverse model for extracting the spatial and temporal variation of strain rate from extensional sedimentary basins is described. Our starting point is a forward model which allows basin stratigraphy to be calculated from any given strain rate distribution. This forward model includes potentially important effects such as flexural rigidity and the two-dimensional conduction/advection of heat. Conversely, inverse modeling determines strain rate variation by minimizing the misfit between predicted and observed patterns of basin subsidence. No a priori assumptions about the number, duration, or intensity of rifting episodes are necessary. Instead, strain rate is allowed to vary smoothly throughout time and space. An important restriction is that vertical lines remain vertical, but this restriction can be relaxed if deemed necessary. We have successfully inverted different synthetic sedimentary basin geometries which were generated by forward modeling. Sensitivity analysis and noise tests demonstrate that strain rate patterns can be recovered with confidence. The relationship between stratigraphic misfit and elastic thickness shows that usually an upper limit, but not a lower limit, for elastic thickness can be retrieved. Our general approach is applicable to any extensional sedimentary basin, including highly extended passive margins, and it should be regarded as the stepping stone to more sophisticated two-dimensional and three-dimensional inverse modeling. In the companion paper, we apply our algorithm to a set of Phanerozoic extensional sedimentary basins located worldwide.