A haptic device using flexible sheet is developed. This device elongates a rubber sheet with four servo motors in parallel. Controlling their motor angles varies softness of the sheet: stretched sheet feels hard, and loose sheet feels soft. Hence a user can feel different softness of virtual objects when he pushes the sheet directly with his finger. We apply this device to haptic feedback of real soft objects. The system consists of the haptic device and a robot with a pressure sensing device. This sensing device is a rubber hemisphere filled with air. The internal pressure is measured when the hemisphere is pressed against an object. First a user pushes the center of the sheet. The movement of the side edge of the sheet is observed with a close-up camera, and the user's pushing pressure on the sheet is estimated. Next the robot pushes a target object so that its pushing pressure on the object, which is measured with the pressure sensing device, may coincide with the user's pushing pressure on the sheet. At the same time, the softness of the object is estimated from the measured pushing pressure on the object and the indentation of the object, which is given by the robot's movement. Then the haptic device controls the motor angles so that the sheet's softness may be equal to the object's softness. The system repeats this process in real time. In this way the user feels the same softness as the real object by pushing the sheet. As an experimental result, the developed haptic device can imitate softness of a real stuffed doll.