Due to their various advantages, interest in the development of covalent drugs has been renewed in the past few years. It is therefore important to accurately describe and predict their interactions with biological targets by computer-aided drug design tools such as docking algorithms. Here, we report a covalent docking procedure for our in-house docking code Attracting Cavities (AC), which mimics the two-step mechanism of covalent ligand binding. Ligand binding to the protein cavity is driven by nonbonded interactions, followed by the formation of a covalent bond between the ligand and the protein through a chemical reaction. To test the performance of this method, we developed a diverse, high-quality, openly accessible re-docking benchmark set of 95 covalent complexes bound by 8 chemical reactions to 5 different reactive amino acids. Combination with structures from previous studies resulted in a set of 304 complexes, on which AC obtained a success rate (rmsd ≤ 2 Å) of 78%, outperforming two state-of-the-art covalent docking codes, genetic optimization for ligand docking (GOLD (66%)) and AutoDock (AD (35%)). Using a more stringent success criterion (rmsd ≤ 1.5 Å), AC reached a success rate of 71 vs 55% for GOLD and 26% for AD. We additionally assessed the cross-docking performance of AC on a set of 76 covalent complexes of the SARS-CoV-2 main protease. On this challenging test set of mainly small and highly solvent-exposed ligands, AC yielded success rates of 58 and 28% for re-docking and cross-docking, respectively, compared to 45 and 17% for GOLD.