The article presents the results of the experimental research on precision measurement of total stopping range and energy deposition function of intermediate and heavy ion beams in cold solid matter. The “thick target” method proves to be appropriate for this purpose. Two types of detectors were developed which provide an error of the total stopping range measurement of less than 3% and of the beam energy deposition function of about 7%. The experiments with 58Ni+26, 197Au+65, and 238U+72 ion beams in the energy range 100–300 MeV/u were performed on SIS-18 (Gesellschaft für Schwerionenforschung, Darmstadt) in 1999–2001. The measured data on the total stopping ranges for the above ion species in bulk and foiled Al and Cu targets are presented. The investigation showed that there is a noticeable discrepancy between the measured stopping ranges and the theoretically predicted ones. Also, it was shown that realistic ion energy deposition depends on the type of target (bulk or foiled). Further investigation is necessary to clarify the latter.