The　relation　between　the　elastic　deformations　and　the　elastic　displacements　of　the　links　of　flexible　planar　robots　is　investigated.　The　elastic　deformations　of　links　are　calculated.　The　Kineto-Elastodynamics　theory　in　conjunction　with　Timoshenko　beam　theory　is　employed　to　derive　the　maximal　dynamic　stress　of　the　links　and　its　position,　considering　the　effects　of　bending-shearing　strain　and　tensile-compression　strain.　The　purpose　of　dynamic　stress　analysis　is　well　illustrated　through　the　numerical　simulation.　Compared　with　the　results　of　SAMCEF　software　simulation,　the　numerical　simulation　results　show　good　coherence　and　advantages　of　the　method.　The　dynamic　stress　analysis　is　demonstrated　to　have　significant　impact　on　the　design　and　control　of　flexible　robots.　©　2006　IEEE.