Circus owner Bobby Roberts was given a three year conditional discharge.
Bobby Roberts was found guilty at Northampton Crown Court of allowing Anne to be chained by her front and rear leg at all times, of failing to take steps to prevent his employee mistreating her and of failing to make sure the needs of a protected animal were met.
The court has been shown footage filmed secretly by animal welfare group Animal Defenders International (ADI) of the animal being beaten at the circus's winter quarters in Polebrook, Cambridgeshire, last year.
The footage, filmed last year, also showed Anne constantly chained to the ground.
The elderly elephant could be seen chained by one foot and one hind leg in a barn. The legs of the animal - who the prosecution allege was not receiving medication for its arthritis - could also be seen to buckle several times.
Mr Roberts told the court he was unaware Anne was constantly chained.
Roberts and his wife also deny a charge of failing to ensure the elephant's needs were met by not giving her medication for her arthritis.