This book consists of certain flows of variable viscosity and variable permeability that are of useful practical applications. The book consists of six chapters. The first chapter in introductory. In Chapter 2 and 3 MHD flow with viscosity variation through an annular pipe in the presence of a radial magnetic field and in the parallel plate channel in the presence of transverse magnetic field has been investigated. In chapter 4 the slow flow of an incompressible viscous fluid past a heterogeneous porous sphere with radial variation of permeability is considered and found analytical solutions. Chapter 5 is devoted to the study of channel flow of a viscous incompressible fluid through a heterogeneous porous medium of linear permeability distribution. In chapter 6 flow of a viscous incompressible fluid in an annular region between two coaxial cylindrical tubes filled with a porous medium of variable permeability distribution is studied.