We use two-dimensional numerical experiments to investigate the long-term dynamics of an oceanic slab. Two problems are addressed: one concerning the influence of rheology on slab dynamics, notably the role of elasticity, and the second dealing with the feedback of slab-mantle interaction to be resolved in part 2. The strategy of our approach is to formulate the simplest setup that allows us to separate the effects of slab rheology (part 1) from the effects of mantle flux (part 2). Therefore, in this paper, we apply forces to the slab using simple analytical functions related to buoyancy and viscous forces in order to isolate the role of rheology on slab dynamics. We analyze parameters for simplified elastic, viscous, and nonlinear viscoelastoplastic single-layer models of slabs and compare them with a stratified thermomechanical viscoelastoplastic slab embedded in a thermal solution. The near-surface behavior of slabs is summarized by assessing the amplitude and wavelength of forebulge uplift for each rheology. In the complete thermomechanical solutions, vastly contrasting styles of slab dynamics and force balance are observed at top and bottom bends. However, we find that slab subduction can be modeled using simplified rheologies characterized by a narrow range of selected benchmark parameters. The best fit linear viscosity ranges between 5 × 1022 Pa s and 5 × 1023 Pa s. The closeness of the numerical solution to nature can be characterized by a Deborah number >0.5, indicating that elasticity is an important ingredient in subduction.