Relative to solid water, electron fluence correction factors at the depth of dose maximum in bone, lung, aluminum, and copper for nominal electron beam energies of 9 MeV and 15 MeV of the Clinac 18 accelerator have been determined experimentally and by Monte Carlo calculation. Thermoluminescent dosimeters were used to measure depth doses in these materials. The measured relative dose at dmax in the various materials versus that of solid water, when irradiated with the same number of monitor units, has been used to calculate the ratio of electron fluence for the various materials to that of solid water. The beams of the Clinac 18 were fully characterized using the EGS4/BEAM system. EGSnrc with the relativistic spin option turned on was used to optimize the primary electron energy at the exit window, and to calculate depth doses in the five phantom materials using the optimized phase-space data. Normalizing all depth doses to the dose maximum in solid water stopping power ratio corrected, measured depth doses and calculated depth doses differ by less than +/- 1% at the depth of dose maximum and by less than 4% elsewhere. Monte Carlo calculated ratios of doses in each material to dose in LiF were used to convert the TLD measurements at the dose maximum into dose at the center of the TLD in the phantom material. Fluence perturbation correction factors for a LiF TLD at the depth of dose maximum deduced from these calculations amount to less than 1% for 0.15 mm thick TLDs in low Z materials and are between 1% and 3% for TLDs in Al and Cu phantoms. Electron fluence ratios of the studied materials relative to solid water vary between 0.83+/-0.01 and 1.55+/-0.02 for materials varying in density from 0.27 g/cm3 (lung) to 8.96 g/cm3 (Cu). The difference in electron fluence ratios derived from measurements and calculations ranges from -1.6% to +0.2% at 9 MeV and from -1.9% to +0.2% at 15 MeV and is not significant at the 1sigma level. Excluding the data for Cu, electron fluence correction factors for open electron beams are approximately proportional to the electron density of the phantom material and only weakly dependent on electron beam energy.