The　ball　screw　with　a　long　stroke　has　small　rigidity　in　radial　direction　and　is　very　liable　to　resonate　dramatically　during　operation　at　high　speed.　For　improving　the　critical　speed　of　the　ball　screw,　this　paper　investigates　the　influence　of　the　supporting　stiffness　of　the　screw　shaft　at　the　nut　on　the　resonance　frequency　of　the　screw　shaft　in　the　radial　direction.　The　screw　shaft　is　modeled　as　an　Euler-Bernoulli　beam　with　elastic　supports　at　both　ends　and　the　position　of　the　nut.　According　to　the　established　model,　the　relationship　between　the　natural　frequencies　and　the　supporting　stiffness　of　the　shaft　at　the　nut　can　be　obtained.　The　simulation　results　show　that　the　flexible　support　at　the　position　of　the　nut　can　effectively　increase　the　minimum　natural　frequencies　and　reduce　the　variation　range　of　the　natural　frequencies　over　the　travel　range　of　the　nut.　It　is　conducive　to　the　vibration　suppression　and　the　critical　speed　improvement　of　the　ball　strew.