Abstract <p>This article studies the motion of a three-link mathematical pendulum with identical parameters of links and end loads, in the joints of which viscous friction with identical dissipative coefficients acts. A linear model of motion of this system is constructed and the corresponding characteristic equation of the sixth degree in dimensionless form is derived, containing one dimensionless dissipative parameter. The case of multiple roots, the case of equal absolute values of the imaginary parts in two pairs of complex-conjugate roots, and the case of coincidence of real parts of two complex-conjugate roots and one real root are studied, and the corresponding values of the dissipative parameter are identified. Based on these values and using numerical procedures, the dependences of all roots of the characteristic equation on this parameter are found and the behavior of the absolute values of their real and imaginary parts is studied, and also the problem of optimizing the damping of system oscillations according to the criterion of maximizing the degree of stability is solved. This article is the first part of the study of the dynamics of a dissipative three-link pendulum, the continuation of which will be presented in the form of a separate work <i>Dynamics of a Three-Link Pendulum with Viscous Friction in the Joints. II. Construction of Dissipative Oscillation and Motion Modes</i>.</p>