Nicknamed "el Peluca" (the wig), Cubías made his debut for El Salvador in a November 1995 friendly match against Yugoslavia and has earned a total of 25 caps, scoring 2 goals. He has represented his country in 2 FIFA World Cup qualification matches and played at the 1995 and 2001 UNCAF Nations Cups and at the 1996 and 2002 CONCACAF Gold Cups.