The paper reports the results of a study of the parallel processes occurring in the billet during the time of changes in the continuous casting process parameters. As found, due to a change in the rate of movement of the billet $f_{\textrm{mov}}$, there are parallel changes in rheological (damage parameter $\omega$) and mechanical properties (ultimate tensile strength $\sigma_{\textrm{TS}}$) processes that occur in the billet. As revealed, the additional thermophysical process exists in the billet such as the growth rate of the thickness $\dot{\xi}$ of the billet crust under variations in $f_{\textrm{mov}}$. It follows there from that the values of $\dot{\xi}$ represent an additional parallel process. A found, the $\dot{\xi}$ and the solidification coefficient $k_{\textrm{sol}}$ are the same thermophysical value, whence it follows that $k_{\textrm{sol}}$ has not a constant value, but depends on the time of solidification or on the reduced thickness of the billet $R_{\textrm{red}}$; $k_{\textrm{sol}}$ = const can only be under the conditions $R_{\textrm{red}}$ = const to determine the $k_{\textrm{sol}}$ of the same metal or alloy; only after that the $k_{\textrm{sol}}$ values for various metals and alloys can be compared. As revealed, the direction of movement while overcoming the static friction force (SFF) affects the investigated properties of the billet: the values of the process parameters of $f_{\textrm{mov}}$ are in direct proportion to the values of the thermophysical properties of the billet of both under the translational and reverse movement of the billet while overcoming the static friction force with the translational movement of the billet, the values of the mechanical properties $\sigma_{\textrm{TS}}$ of the billets are in inverse proportion to the values of the investigated processes such as $\dot{\xi}$, $\omega$, and $f_{\textrm{mov}}$; with the reverse movement of the billet, the values of the processes $\dot{\xi}$, $\omega$, and $f_{\textrm{mov}}$ are in direct proportion to the values of the mechanical properties $\sigma_{\textrm{TS}}$ of the billets; with the reverse movement of the billet, a decrease in the damage parameter of the billet in the cycle is observed, which makes it possible to increase the values of $\sigma_{\textrm{TS}}$. As shown, the values of the mechanical properties of $\sigma_{\textrm{TS}}$ of the billets can simultaneously affect two process parameters, the speed of movement $V_{\textrm{mov}}$ and the time of movement $t_{\textrm{mov}}$ of the billet in the cycle at $f_{\textrm{mov}}$ = const. As revealed, the direction of movement of the billet while overcoming SFF is a trigger to start the process of reducing the damage parameter in the billet during the transition from translational to reverse movement. As shown, if the following parallel processes of $f_{\textrm{mov}}$, $\dot{\xi}$ and $\sigma_{\textrm{TS}}$ are in direct proportion, then it is possible to predict the values of $\sigma_{\textrm{TS}}$ by using both the values of $f_{\textrm{mov}}$ and $\dot{\xi}$.