The partial differential equations arising in the study of non-Newtonian fluids offer many challenges not only to physicists and numerical analysts but also mathematician alike. Particularly the studies regarding the unsteady flows due to a stretching sheet is very scarce in the literature. Much attention has been given to the steady flow problems. Few attempts have been made regarding the unsteady flows. The main aim here is to develop the analytic series solutions using homotopy analysis method. One important aspect of these solutions is that these solutions are valid for all the dimensionless time values as most of the numerical solutions does not. In this particular book we have emphasized on the viscous and second grade fluids both for linearly and radially stretching sheets.