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.