Westudythebucklingofaonefibercompositewhosematrixstifnessisslightlydependentonthecompressiveforce.Weshowthattheequilibriumcurvesofthesystemexhibitalimitloadwhentheinducedstifnessparametergetsbiggerthanathreshold.Thislimitloadincreaseswhenthestifnessparameterisincreasinganditisrelatedtoapossiblelocalizedpathinthepost-bucklingdomain.Suchachangeinthemaximumloadmaybeverydesirablefromastructuralstandpoint.