Nowadays traffic flow and congestion is one of the main societal and economical problems related to transportation in industrialized countries. Traffic congestion is one of the greatest problems in Bangladesh also. Our aim is to understand and develop an optimal road network with efficient movement of traffic and minimal traffic congestion problems, accidents and pollutions etc. This book therefore considers the macroscopic traffic flow model known as LWR model ,appended with a closure linear velocity-density relationship which provides a first order hyperbolic partial differential equation (PDE) and is treated as an initial boundary value problem (IBVP).we present the analytic solution of the traffic flow model as a Cauchy problem. The existence and uniqueness of the traffic flow model is also presented here.A numerical simulation of the traffic flow model (IBVP) is performed based on a finite difference scheme for the model with a suitable numerical scheme of the IBVP for this is the Lax-Friedrichs scheme and establish well-posedness and stability condition for the scheme. We implement the numerical scheme by computer programming language.