Current elbow prosthesis design and fabrication is not catering for the target population, leading to a prevalent occurrence of prosthesis mismatch in total elbow arthroplasty (TEA) surgeries. To address this challenge, it is crucial to develop an efficient elbow joint classification method that accurately captures specific morphological variations, advancing the design of diverse prostheses for optimal matching. In this paper, we introduce two classification algorithms utilizing shape features extracted from the Riemannian manifold and anatomical features derived from three-dimensional (3D) measurements. Additionally, we quantitatively evaluate these feature-based algorithms using computed tomography (CT) scan images from a randomly recruited sample of 120 individuals registered to a local hospital. This study represents the first endeavor in classifying and evaluating elbow joints through shape and anatomical features. Our results demonstrate that the shape-based classification algorithm not only provide a better understanding of morphological variations with improved cluster compactness and separability, but also captures crucial clinical variations such as gender differences.