A flexible acetabular cup is provided which has an inner bearing surface which comprises a substantially part-spherical portion and two independent arms projecting therefrom. The arms form a separation or opening in the rim of the cup with the external surface of the cup being shaped to cause the independent arms to be pre-stressed towards each other when the cup is inserted in place in a pre-prepared acetabular socket. One way of accomplishing this is to form the cup with the arms bowed outwardly at the time of manufacture.