Various kinds of jamming phenomena are observed in our daily life. In particular, a traffic jam on a motorway is a very familiar phenomenon and attracts a lot of researchers due to its possibility of new insights into collective dynamics of interacting particles. In this book, we have investigated the jamming formation, i.e. shock wave formation in two new models : one describes the dynamics of one-dimensional traffic flow on a motorway as a compressible fluid model, so-called “macroscopic” approach, based on the dynamical wave theory, and the other describes the dynamics of public conveyance system as a stochastic cellular automaton model so-called “microscopic” approach. The former topic includes mathematical and physical significance to get to the essence of the mechanism of traffic jam without bottlenecks and the latter topic includes the practical applications as contribution to society of mathematical science.