Composition depth profiles of the outer 50 angstrom of plasma-fluorinated poly(ethylene terephthalate) fibers were obtained by angle-dependent X-ray photoelectron spectroscopy (XPS). The effect of sample geometry on XPS sampling depth and the depth distribution function (DDF) was determined theoretically for cylindrical and hemispherical surfaces. The theoretical DDFs are nonexponential. For cylindrical surfaces, the effect is small, a 22% increase in surface sensitivity. The average XPS sampling depth for smooth, properly oriented fibers is shown to vary, as it does for a planar surface, as the sine of the nominal takeoff angle. The DDF appropriate for cylindrical surfaces was incorporated into a computer program for inversion of angle-dependent XPS data to obtain composition depth profiles of the fibers. Plasma-fluorinated PET fibers were used to demonstrate the use of angle-dependent XPS on fibers. XPS results indicate that most fluorination occurs within the top few "monolayers," attack is preferentially at the phenyl ring, both -CHF- and -CF2- moieties are formed, and fluorination causes partial loss of aromaticity.