This　paper　presents　a　nonlinear　vibration　model　of　rolling　element　bearings　with　5　degrees　of　freedom　based　on　Hertz　contact　theory　and　relevant　bearing　knowledge　of　kinematics　and　dynamics.　The　slipping　of　ball,　oil　film　stiffness,　and　the　nonlinear　time-varying　stiffness　of　the　bearing　are　taken　into　consideration　in　the　model　proposed　here.　The　single-point　local　fault　model　of　rolling　element　bearing　is　introduced　into　the　nonlinear　model　with　5　degrees　of　freedom　according　to　the　loss　of　the　contact　deformation　of　ball　when　it　rolls　into　and　out　of　the　local　fault　location.　The　functions　of　spall　depth　corresponding　to　defects　of　different　shapes　are　discussed　separately　in　this　paper.　Then　the　ode　solver　in　Matlab　is　adopted　to　perform　a　numerical　solution　on　the　nonlinear　vibration　model　to　simulate　the　vibration　response　of　the　rolling　elements　bearings　with　local　fault.　The　simulation　signals　analysis　results　show　a　similar　behavior　and　pattern　to　that　observed　in　the　processed　experimental　signals　of　rolling　element　bearings　in　both　time　domain　and　frequency　domain　which　validated　the　nonlinear　vibration　model　proposed　here　to　generate　typical　rolling　element　bearings　local　fault　signals　for　possible　and　effective　fault　diagnostic　algorithms　research.