Extension of flat films uneven in thickness and lying on the (x,y) plane is analyzed mathematically. Constitutive models assumed are isothermal Newtonian fluids and rubber‐like elastic solids. Governing equations reduce to the Cauchy–Riemann equations when the material is Newtonian fluid and the film is uniform in thickness. Many unusual modes of extension exist in this case. In both cases of Newtonian fluids and rubberlike elastic solids, governing equations reduce to readily solvable ordinary differential equations when the extension is axisymmetrical. Conditions of wrinkle free extension are introduced. Numerical solutions are obtained for the general extension of the films of rubber‐like elastic solids.