You can see wild elephant in the jungle by travelling in a jeep. Minneriya is very famous for safari and some times you will see wild elephants on the main road itself. There will be a guide allocated for each vehicle from the entrance gate and he will guide your vehicle to the proper locations to enjoy this once in a life time experience.
Jeeps are available in the area to hire. It is difficult for a car to travel on these gravel roads within the jungle. You will be able to see few other animal types also who are common to the area.