This book presents the stream-tube method (STM), a method offering computational means of dealing with the two- and three-dimensional properties of numerous incompressible materials in static and dynamic conditions. The authors show that the kinematics and stresses associated with the flow and deformation in such materials can be treated by breaking the system down into simple computational sub-domains in which streamlines are straight and parallel and using one or two mapping functions in steady-state and non- steady-state conditions. The STM is considered for various problems in non- Newtonian fluid mechanics with different geometries. The book makes use of examples and applications to illustrate the use of