Spectral distortions that arise in evanescent-wave absorption spectra obtained with multimode step-index optical fibers are analyzed both theoretically and experimentally. Theoretical analysis is performed by the application of Kramers-Kronig relations to the real and the imaginary parts of the complex refractive index of an absorbing external medium. It is demonstrated that even when the extinction coefficient of the external medium is small, anomalous dispersion of that medium in the vicinity of an absorption band must be considered. Deviations from Beer's law, band distortions, and shifts in peak position are quantified theoretically as a function of the refractive index and the extinction coefficient of the external medium; the effect of bandwidth for both Lorentzian and Gaussian bands is also evaluated. Numerical simulations are performed for two types of sensing sections in commonly used plastic-clad silica optical fibers. These sensors include an unclad fiber in contact with a lower-index absorbing liquid and a fiber with the original cladding modified with an absorbing species. The numerical results compare favorably with those found experimentally with these types of sensing sections.