This study focuses on analytical models for stress prediction of periodontal ligament in orthodontic therapy. Orthodontics as specialist branch of dentistry is introduced in the first chapter. The primary goals and current choices of treatment as their advantages and disadvantages are listed in introductory chapter. The second chapter presents the classification and morphology of the teeth and describes the structure and function of the teeth as well as the surrounding tissues. Periodontal ligament and alveolar bone are particularly emphasized as they play a significant role in orthodontic tooth movement. The basic concepts of orthodontic therapy are presented in the third chapter. To fully understand the process of orthodontic tooth movement, it is necessary to explain the biomechanics behind the tooth movement, as well as the term center of tooth resistance. Chapter four covers the development of analytical models. The root of the tooth was approximated by two models, namely the paraboloid and the elliptical paraboloid. Certain assumptions and limitations of the model were introduced, on the basis of which analytical formulas were obtained. The excerpt was performed using the classical theory of elasticity, referring to the horizontal translation of a single root tooth. Section five presents the results of the stress analyzes performed for both models. The distribution of stress components is shown: graphically, by equation and in tabular form. As the same dimensions and properties of periodontal ligament were used for both models, the obtained results were compared by relative difference. Subsequently, the graphical distribution and results of the comparison were supported by the evidence. Finally, a conclusion is made based on the performed stress analyzes.