The longevity of implanted artificial hip joint is dependent on wear debris caused by the transient stress occurring repeatedly on the inner hemispherical surface and its neighborhood and the change in clearance due to the deformation in UHMWPE cup. In this study, three-dimensional elastic deformations and stresses in a hemispherical acetabular cup made of UHMWPE and subjected to an asymmetric load on the inner hemispherical surface are analyzed by the use of Papkovich-Neuber displacement function. Effects of the loaded position in meridian direction on the deformations and stresses in the UHMWPE cup are quantitatively discussed based on the numerical results of the analytical solution.