With　the　increasing　applications　of　the　planetary　roller　screw　mechanism　(PRSM)　in　mechanical　systems　particularly　machine　tools,　a　comprehensive　mathematical　model　is　required　to　define　the　kinematic　characteristics　and　relations　of　the　PRSM,　such　that　its　performances　can　be　predicted　for　reliability　analysis　and　design　of　machine　tools.　In　this　paper,　the　influences　of　machining　and　assembly　errors　on　the　motion　characteristics　of　the　PRSM　are　analyzed,　and　the　kinematic　model　of　the　PRSM　is　established　considering　runout　errors　and　elastic　deformation.　The　planetary　roller　screw　mechanism　can　be　considered　as　a　spring-mass　system　for　analysis　of　the　elastic　deformation　of　the　ball　screw＇s　thread　under　inertial　force.　For　the　spring-mass　system,　adjacency　matrix　is　introduced　to　define　the　relationships　between　the　elastic　displacements　of　the　joints　and　the　deformations　of　the　elements.　Then,　by　considering　the　balance　of　force　and　the　coordination　of　deformation,　the　nonlinear　motion　model　of　the　double-nut　roller　screw　is　established.　The　effectiveness　of　the　proposed　model　is　verified　by　comparing　the　analytical　results　with　the　experimental　data.