The paper deals with critical threshold phenomena in a dynamic continuum traffic flow model. The Cauchy problem for the hyperbolic system \(\rho _t+(\rho u)_x=0,\) \(u_t+uu_x+\frac{1}{\rho}p(\rho)_x=\frac{1}{\tau}(v_e(\rho)-u),\) where \(p(\rho)=c_0^2\rho,\) \( v_0(\rho)=c_0\ln \frac{1}{\rho},\) \( 0<\rho \leq 1,\) is considered. The authors derive a priori estimates of the derivatives of the Riemann invariants in order to identify the upper threshold for global existence of smooth solutions and lower threshold for finite time singularity formation.