In the recent past, the rapid growing number of vehicles on long crowded roads elicited
rigorous scienti c research activities in the eld of tra c ow modeling. In this thesis
we present and discuss some of the macroscopic models of vehicular tra c ow; here we
discuss Payne-Whitham(P-W) and the Aw-Rascle models of tra c ow both of which are
second order. We study the Riemann problems of these models. The numerical method
developed here is the nite volume method (FVM), more speci cally the Godunov-type
approximation together with the CFL condition for stability test of solutions.