Inhibition of the main protease 3CLpro of SARS-CoV and SARS-CoV-2 is being targeted in the search for antivirals to shorten patient recovery times from Covid-19 disease. We investigated 72 flavonoids for their potential to bind with the active catalytic site of 3CLpro for SARS-CoV and SARS-CoV-2. In silico molecular dynamics docking was performed using energy-minimized states of the flavonoids. Three variants of the active catalytic site of the protease 3CLpro were used: one based on x-ray crystallography for SARS-CoV, the second based on x-ray crystallography for SARS-CoV-2, and the third based on a 3D-modeled form of an amino acid sequence alignment of SARS-CoV-2 3CLpro 2 from 8 humans. Docking involved characterization of the best putative pose in the “pocket” of the active site based on altering rotatable bonds in each molecule. The binding energy (kcal/mol) and number of hydrogen bonds were assessed during each pose. Mean binding energy across the 3 variants of 3CLpro was sorted in ascending order to rank each flavonoid, since more negative values indicate stronger binding. The top 10 flavonoids identified were amentoflavone, gallocatechin gallate, diosmin, epigallocatechin gallate, hidrosmin, catechin gallate, elsamitrucin, pectolinaren, quercetin, and isoquercetin. Other flavonoids investigated with significant binding energies were hesperidin, rutin, rhoifolin, and peurarin. In vivo animal research is now needed for evaluating whether these flavonoids can minimize early infection and alleviate symptoms and shorten recovery times for late-stage Covid-19 disease. Human prevention trials for minimizing early infection and combination therapy trials with antivirals for shortening recovery times in late-stage Covid-19 disease could also be pursued.