The study proposes a new mathematical model describing the performance of the mechanical spinning system on the ring spinning machine. The mechanical spinning system considered in the study is formed of the following elements: the reinforced spindle-package assembly; the ring solidary with the ringrail segment corresponding to a spindle, and the traveller. The simplifying working assumption adopted in the present study restrict only to a certain extent the general character of the dynamic problem considered, comparatively with the classical models. Settlement of the motion equations of the mechanical spinning system is based on Lagrangean formalism. The mathematical model thus established provides solutions to all problems studying the performances of the mechanical spinning system, both in a transitory and in a permanent regime, the differential motion equations permitting the establishment of the conditions – the driving ones, especially – the stresses should meet, so that yarn’s twisting should occur as a stationary process.