- Superconducting tape coils and Roebel cables are often modeled as stacks of parallel superconducting tapes carrying the same transport current. We solved, in the infinitely thin approximation, the transport current and magnetization problems for such stacks using an efficient numerical scheme based on a variational formulation of the Kim critical-state model. We also refined the anisotropic bulk approximation, introduced by Clem et al in order to simplify AC loss estimates for densely packed stacks of many tapes; this was achieved by removing the simplifying a priori assumptions on the current sheet density in the subcritical zone and the shape of this zone boundary. Finally, we studied the convergence of stack problem solutions to the solution of the modified bulk problem. It was shown that, due to the fast convergence to the anisotropic bulk limit, accurate AC loss estimates for stacks of hundreds of tapes can usually be obtained also using a properly rescaled model of a stack containing only ten to twenty tapes.