The radiation dose from galactic cosmic rays during a manned mission to Mars is expected to be comparable to the allowable limit for space shuttle astronauts. Most of this dose would be due to galactic cosmic rays with energies <1 GeV nucleon-1, with important contributions from heavy nuclei in spite of their low abundance relative to H and He. Using instruments on NASA's Advanced Composition Explorer (ACE) spacecraft, we have made the most statistically precise measurements to date of the solar minimum energy spectra of cosmic ray nuclei with charge Z=4--28 in the energy range ~40--500 MeV nucleon-1. We compare these measurements obtained during the 1997--1998 solar minimum period with measurements from previous solar minima and with models of the near-Earth radiation environment currently used to perform shielding and dose calculations. We find that the cosmic ray heavy-element spectra measured by ACE are as much as 20% higher than previously published solar minimum measurements. We also find significant differences between the ACE measurements and the predictions of available models of the near-Earth radiation environment, suggesting that these models need revision. We describe a cosmic ray interstellar propagation and solar modulation model that provides an improved fit to the ACE measurements compared to radiation environment models currently in use. ¿ 2001 American Geophysical Union