On February 26, 2000, the 12-day, 18th historic eruption of Hekla volcano in Iceland began with an explosive Subplinian eruptive column and pyroclastic basaltic flows fed by column collapses (Höskuldsson et al., 2007). Interferometric synthetic aperture radar (InSAR) captured the deformation pattern associated with the movement of a shallow fissure (i.e. dike) during the eruption (Ofeigsson et al., 2011). These data present the opportunity to use inverse methods to estimate parameters describing the behavior of the eruptive fissure (Fukushima et al., 2010, Anderson and Segall, 2011, Ofeigsson et al., 2011). I use the 2000 eruption of Hekla as an example in linear inversions that investigate the influence of topography and layered rock properties in 3-D finite element models (FEMs) on estimates of parameters associated with the fissure movement. FEMs are used for this study because they are the best type of model which allow for arbitrary geometric configurations of the domain and effectively satisfies the static elastic governing equations. The results of the study are: 1. FEMs of fissure movement are sensitive to a free-surface geometry representing topography but less sensitive to rock property distribution. 2. The estimated magnitude of each movement responds differently to unique inputs. Including topography increased estimates of strike-slip motion and decreased estimates of opening relative to a homogeneous elastic half-space model or a layered elastic half-space model. 3. Including topography directly into the model domain allows exploration of arbitrary dike geometry, such as a dike which changes strike, which is not possible with HEHS assumptions and topographic corrections, but is indicated in this study. The flexibility and power of FEMs far outweighs the computational burden they used to present. The results of this study will guide future modelers to required steps to build the most accurate and efficient model to estimate parameters related to fissure behavior during an eruption. These results can help elucidate the plumbing system of a volcano, including the relationship between processes in the magma chamber and in the conduit during an eruption. This can help geologists, volcanologists, and hazard assessment teams assemble more accurate eruption forecasts.