This paper applies two powerful analytical approximation methods to the jamming transition problem (JTP) of traffic flow networks. The governing equations are modeled on the Lorentz system and take the form of a nonlinear nonconservative oscillator. We describe and implement the homotopy perturbation method (HPM) and the variational iteration method (VIM) to compute approximations to the JTP solution. Their solutions are compared with the purely numerical fourth-order Runge–Kutta solution. We conclude that both HPM and VIM provide highly accurate analytical solutions to the nonlinear jamming transition problem.