Molecular docking is a computational approach for predicting the most probable position of ligands in the binding sites of macromolecules and constitutes the cornerstone of structure-based computer-aided drug design. Here, we present a new algorithm called Attracting Cavities that allows molecular docking to be performed by simple energy minimizations only. The approach consists in transiently replacing the rough potential energy hypersurface of the protein by a smooth attracting potential driving the ligands into protein cavities. The actual protein energy landscape is reintroduced in a second step to refine the ligand position. The scoring function of Attracting Cavities is based on the CHARMM force field and the FACTS solvation model. The approach was tested on the 85 experimental ligand-protein structures included in the Astex diverse set and achieved a success rate of 80% in reproducing the experimental binding mode starting from a completely randomized ligand conformer. The algorithm thus compares favorably with current state-of-the-art docking programs.