In this study the basic model is formulated to show the effect of blocking on the dynamics of vehicles flows on the road. The dynamics of vehicles flows have been described using deterministic nonlinear dynamical system. The study divided the total number of vehicles on the road into four exclusive compartments as Free –– Slow – Average – Released vehicles. The well-posedness of formulated model for vehicles flows on the road has been verified. The equilibrium points of formulated model have been identified. Further, to observe the effect of blocking in the vehicles population flows the retardation number is used. The local and Global stability of equilibrium points of the formulated model equations has been analyzed using modified Castilo Chavez approach and Hurwitz criteria. The qualitative behavior of solutions of formulated dynamical system has been described by using a MATLAB software.