A finite element modeling (FEM) approach is carried out to estimate the contact stresses such as von-Mises and shear stress on the acetabular cup liner, made up of ultra-high molecular weight polyethylene (UHMWPE)-hydroxyapatite (HAp)-carbon nanotubes (CNT) based composites. The highlights of this work include the effects of liners' material (UHMWPE-HAp-CNT composites), radial clearance (0.05 to 1 mm), and liners' wall thickness (3 to 8 mm) on contact stresses. The thick liner (thickness: 8 mm) with conformal geometry (radial clearance 0.05 mm) produced the lowest contact stresses (von-Mises: 13.8-17.5 MPa and shear stress: 2.3-3.3 MPa). In contrast, the thin liner (thickness: 3 mm) with higher radial clearance (1 mm) showed the highest von-Mises stress (78.6-131.0 MPa) and shear stress (17.0-23.3 MPa). According to ISO 7206-1, nearly 6-7 times reduced contact stresses were observed because of the wider articulating contact area provided by thick cup liner and its conformity with respect to the femoral head. The UHMWPE-2 wt % CNT composite (UC) showed low von-Mises stress (16.1 MPa) and lowest shear stress (2.3 MPa); thus, it is the most damage tolerant material (wear rate: 2.6 × 10^-7 mm³/Nm). The excellent mechanical properties such as hardness (165 MPa), elastic modulus (2.28 GPa), and tensile strength (36.7 MPa) are reasoned to elicit an increased sliding-wear resistance of UC. Thus, CNT-based UHMWPE composite can be the potential acetabular cup liner with a thickness of 8 mm and clearance of 0.05 mm without plastic deformation.