The　dynamics　of　piezoelectric　stick–slip　actuators　is　important　for　structural　optimization　and　positioning　control,　yet　challenging　to　model　because　of　the　potentially　inconsistent　stepping　of　these　actuators　in　the　forward　and　backward　directions.　This　step　inconsistency　is　found　to　be　strongly　associated　with　the　inconsistent　dynamic　response　of　the　piezoelectric　feeding　element　arising　from　the　contact　behavior　between　the　piezoelectric　stack　and　its　flexure-based　preload　mechanism.　With　this　understanding,　an　improved　dynamical　model　for　the　typical　stick–slip　actuator　is　established　in　which　a　non-smooth　contact　model　is　introduced.　A　prototype　was　built　and　tested,　and　with　it　the　contact　behavior　was　proved　to　cause　the　inconsistent　responses　of　the　piezoelectric　feeding　element,　which　in　turn　was　verified　to　cause　the　inconsistent　stepping　characteristics　of　the　stick–slip　actuator.　The　simulated　results　obtained　using　the　proposed　model　were　in　good　agreement　with　the　stepping　curves　of　the　slider　in　bi-directional　motion　under　different　working　conditions.　The　proposed　model　provides　a　new　perspective　to　explain　and　model　the　step　inconsistency　for　stick–slip　actuators　in　bi-directional　motion,　and　has　great　potential　in　aiding　the　design　and　control　of　stick–slip　actuators　for　bi-directional　driving.　©　2020　Elsevier　Ltd