The diseases and injuries of the knee joint are the most common orthopedic disorders. Personalized knee models can be helpful in the process of early intervention and lasting treatment techniques development. Fully automatic reconstruction of knee joint anatomical structures from medical images (CT, MRI, ultrasound) remains a challenge. For this reason, most of state-of-the-art knee joint models contain simplifications such as representation of muscles and ligaments as line segments connecting two points which replace attachment areas. The paper presents algorithms for automatic detection of such points on knee CT images. This paper presents three approaches to automatic detection of ligaments and tendons attachment sites on the patients CT images: qualitative anatomical descriptions, analysis of bones curvature, and quantitative anatomical descriptions. Combinations of these approaches result in new automatic detection algorithms. Each algorithm exploits anatomical peculiarities of each attachment site, e.g., bone curvature and number of other attachments in a neighborhood of the site. The experimental dataset consisted of 26 anonymized CT sequences containing right and left knee joints in different resolutions. The proposed algorithms take into account bone surface curvatures and spatial differences in locations of medial and lateral parts of both knees. The algorithms for detection of quadriceps femoris, popliteus, biceps femoris tendons, and lateral collateral and medial collateral ligaments attachment sites are provided, as well as examples of their application. Two algorithms are validated by comparison with known statistics of ligaments lengths and also using ground truth annotations for anatomical landmarks approved by clinical experts. The algorithms simplify generation of patient-specific knee joint models demanded in personalized biomechanical models. The algorithms in the current implementation have two important limitations. First, the correctness of the produced results depends on the bones segmentation quality. Second, the presented algorithms detect a point of the attachment site, which is not necessarily its center. Therefore, manual correction of the attachment site location may be required for attachments with relatively large area.