The couple from Oundle deny causing unnecessary suffering and failing to prevent an employee from repeatedly beating Anne.
They also deny failing to ensure the elephant's needs were met.
Opening the case for the prosecution, Helen Law played video footage - filmed by Animal Defenders International (ADI) - which showed the animal being kicked and hit with a pitchfork by staff.
The legs of the animal, who the prosecution allege was not receiving medication for arthritis, could also be seen to buckle several times in the footage filmed covertly by the animal welfare organisation.
The video, filmed between 21 January and 15 February last year, showed the Asian elephant chained by one foot and one hind leg in a barn on Bobby Roberts Super Circus in Polebrook.
It also showed Bobby Roberts supervising the chains being swapped from opposing leg to opposing leg by the groom, and him kicking the elephant's trunk.
Footage filmed 14 days later showed the groom kicking the animal's trunk. The elephant can be seen to be kicked in the side and struck with a pitchfork several times during the footage. She can also be seen to be kicked in the trunk on a number of occasions.
"The footage shows a near-on absolute lack of supervision from Bobby Roberts," Ms Law told the court.
"Bobby Roberts was quite happy to authorise casual violence towards the elephant." She alleged the groom was trained to hit the animal and keep Anne chained to the ground.
Bobby Roberts said the members of staff were adequately trained, she added. Mr Roberts said the groom did not follow his orders and he was unable to supervise him due to health problems which stopped him working in the barn as much, Ms Law said.
The trial continues.
All of the animals forced to live in circuses – tigers, lions, bears, elephants, etc. live out their whole lives deprived of freedom and in the majority of cases only come out of their cages or boxes or are released from their chains to be forced to perform ridiculous tricks. These animals are individuals who would travel hundreds of miles if they could in search of food or shelter, and for whom not being able to enjoy their lives causes unimaginable suffering.
Forcing any animal to perform for human entertainment is unethical and cannot be justified. There is no need to keep animals in captivity for our own enjoyment or entertainment, and with your help it’s possible to ban animal circuses in every country. Firstly we should show our rejection of the use of animals as entertainment by not going to animal circuses, zoos, or other places where animals are used for this purposes.
You can learn alot about the natural behaviour of animals by visiting websites, watching documentaries, reading books, and respectfully observing animals in their natural habitat. But perhaps the best lesson is one of respect, so we can recognise that even though we are different in some ways, we are equal.
You can also help animals by encouraging others not to visit these places, talking with your friends and family, handing out our leaflets on speciesism,and volunteering your time with Animal Equality.
For more information visit: www.animalequality.net/entertainment/circuses