The study of a fluid film sprayed on a stretching sheet is important in film cooling and spray coating. This paper considers the similarity solution to the fluid film on a three-dimensional stretching sheet, which includes a new axisymmetric stretching sheet as a special case. The nonlinear problem exhibits uniqueness, non-uniqueness and non-existence properties. Of special interest is the film on a sheet that is stretching in one direction and shrinking in another direction. For some shrinking rates, the film can maintain a free surface of constant depth. Approximate analytic solutions for flow and heat transfer are derived for a small film depth and for large Prandtl numbers.