Equations governing the transient stretching of thin plane film of isothermal Newtonian fluids were introduced in both Cartesian and cylindrical coordinates. Using the equations in Cartesian form, it was shown that uniform film thickness is maintained only when the film is initially uniform in thickness and the deformation is uniform biaxial extension/contraction independent of position (x,y) describable by a stretch ratee11(t)in thexdirection ande22(t)in theydirection wheretis time. Furthermore, the stretching is free of wrinkling or three‐dimensional buckling when the conditionse11+2e11>0and2e11+e22>0are both satisfied. In the one‐dimensional case of axisymmetrical stretching the governing equations in cylindrical coordinates reduce upon Lagrangian transformation to a single partial differential equation inf(u,t),wherefis the present radial position of fluid element anduis its initial radial position. Numerical solutions of this equation show that deviation of deformation from uniform biaxial stretching affect thickness uniformity only slightly, and when annular dent is given to initial thickness profile the shape of dent profileH(u)remains almost unchanged while in stretching.