In the International Atomic Energy Agency's (IAEA) code of practice (TRS 398) and the American Association of Physicists in Medicine's dosimetry protocol (TG-51), full-scatter water phantoms are recommended for the determination of the absorbed dose for both photon and electron beams and, consequently, for the calibration of the user's ionization chambers. This procedure is applied in the Secondary Standard Dosimetry Laboratory, where the calibration is performed on a 60Co gamma beam, in comparison with reference chambers whose absorbed dose-to-water calibration coefficients, ND,w, are known. In this work, we present the results of the calibration of 10 Farmer-like ionization chambers calibrated in three water phantoms (sizes 20 x 20 x 15 cm3, 30 x 30 x 30 cm3, and 35 x 35 x 37 cm3) and two plastic phantoms (size 20 x 20 x 20 cm3) polymethyl methacrlyate (PMMA) and polystyrene). Calibrations are performed by the substitution method using an ionization chamber whose ND,w has been supplied by the IAEA's reference laboratory. It is shown that the results, expressed as the percentage ratio of the calibration coefficient in a given phantom to that of the standard IAEA phantom, is less than 0.35% for all investigated chambers, and that the standard deviation of the mean of the ND,w calibration coefficients determined in all five phantoms is less than 0.06%, except for one nylon-walled ionization chamber, where the observed 0.34% value could be explained by the hygroscopic properties of nylon. Furthermore, a chamber-to-chamber dependence of the calibration coefficient has been shown to vary by up to 2.8%. These results emphasize that the phantom dimensions and its material are not sensitive criteria for the calibration of cylindrical ionization chambers in terms of absorbed dose to water. The results also show that generic calibration coefficients could not be considered for a given type of chamber.