The difference between technical and living systems. Multifunction od human body structures. Human body as a mechanical system with finite degrees of freedom. Differential variational principles. Generalized coordinates and velocities. The Lagrange equations for holonomic and non-holonomic systems. The canonical equations of Hamilton. Kane's equations. Quasi-coordinates. The Gibbs'Appell equations. Acceleration energy. The integral variational principle of Hamilton. Applications of fractional calculus in biomechanics. Rheological properties of human tissue and tissues used in restorations of human body functions. Parameter identification in rheological models of tissues and biomaterials. Collisions and oscillations in biosystems. Muscle force models. Dynamical models of middle ear and energy dissipation within ossicular chain. Specifity of mathematical models and numerical simulations of human body motion: models of humam joints, head-neck connection, and knee. Friction models in biomechanics. Collision models and response of the head-neck system to frontal impact, applications of the Laplace transform method. Applications in rehabilitation, sports and exercise. Artificial devices used to replace functions of human body elements. Applications of Pontrygin's maximum principle in prosthetics design. Statics of deformable bodies and deformations of the skeletal system elements. Applications of the mathematical theory of elastic rods and the method of finite elements in biomechanics.