This book provides comprehensive analysis of Walters-B Viscoelastic flow past a vertical plate. Owing to the significance of this problem in chemical and medical biotechnological processing (e.g. medical cream manufacture) we study the transient case of such a flow in the present paper using the robust Walters-B viscoelastic rheological material model. A Crank-Nicolson finite difference scheme is utilized to solve the unsteady dimensionless, transformed velocity, thermal and concentration boundary layer equations in the vicinity of the vertical plate and the results are discussed in detail. It helps researchers, students, engineers and scientists who work in the area of non-Newtonian fluid flows.