We report all-atom molecular dynamics and replica exchange molecular dynamics simulations on the unbound human immunodeficiency virus type-1 (HIV-1) transactivation responsive region (TAR) RNA structure and three TAR RNA structures in bound conformations of, in total, ∼250 ns length. We compare the extent of observed conformational sampling with that of the conceptually simpler and computationally much cheaper constrained geometrical simulation approach framework rigidity optimized dynamic algorithm (FRODA). Atomic fluctuations obtained by replica-exchange molecular dynamics (REMD) simulations agree quantitatively with those obtained by molecular dynamics (MD) and FRODA simulations for the unbound TAR structure. Regarding the stereochemical quality of the generated conformations, backbone torsion angles and puckering modes of the sugar-phosphate backbone were reproduced equally well by MD and REMD simulations, but further improvement is needed in the case of FRODA simulations. Essential dynamics analysis reveals that all three simulation approaches show a tendency to sample bound conformations when starting from the unbound TAR structure, with MD and REMD simulations being superior with respect to FRODA. These results are consistent with the experimental view that bound TAR RNA conformations are transiently sampled in the free ensemble, following a conformation selection model. The simulation-generated TAR RNA conformations have been successfully used as receptor structures for docking. This finding has important implications for RNA-ligand docking in that docking into an ensemble of simulation-generated RNA structures is shown to be a valuable means to cope with large apo-to-holo conformational transitions of the receptor structure.