The design of the inertial continuously variable transmission consists of the inertial pulsed mechanism with unbalanced inertial elements and two overrunning clutches. The inertial pulsed mechanism is well developed and possesses high reliability. The overrunning clutches are the least reliable parts of the transmission and limit wide application of the transmission. In this paper, a new design of the inertial transmission with only one overrunning clutch is proposed. This transmission provides a high level of the load capability. The object of the investigation is a structural dynamic analysis of the continuously variable automatic inertial mechanical transmission. The physical and mathematical models of this transmission are developed. For these models of this transmission the differential equations of structural dynamics in the form of second kind Lagrange's equations were developed. These nonlinear differential equations were solved on the basis of Runge-Kutta numerical method. The periodic solutions of the equations were also developed by means of the numerical methods. Optimal working modes of the transmission were found using these periodical solutions.