This　paper　presents　a　three-dimensional　analytical　solution　for　the　magnetic　field　distribution　of　permanent　magnet　mechanisms　with　rectangular　magnets.　The　model　is　based　on　the　magnetic　vector　potential　theory　for　the　permanent　magnet　via　the　equivalent　current.　Analytical　expressions　of　the　magnetic　flux　intensity　for　a　single　magnet　and　the　total　magnets　are　deduced.　Green　formula　and　Simpson　method　are　applied　to　solve　the　analytical　expressions.　The　results　agree　well　with　those　calculated　by　the　finite　element　method.　The　proposed　analytical　model　can　provide　a　reference　for　the　design　and　optimization　of　permanent　magnetic　mechanisms　with　rectangular　magnets.　©　2024　IEEE.