 Their biggest success in the Yugoslav Cup, came on season 2001-02 – in the 1/16 finals, they won against Napredak Kruševac, but Mladost were eliminated in the 1/8 finals, away against Radnički Obrenovac.Same success, Mladost made on season 2005-06.In the first phase of Cup of Serbia and Montenegro, Mladost surprisingly won against the First League member Voždovac ("2–1"), and in the 1/8 finals, club from Podgorica lost in last minutes against most successful Serbian club Crvena Zvezda in Belgrade (1–2).