The Transport Collaboration, consisting of researchers from institutions in France, Germany, Italy and the USA, has established a program to make new measurements of nuclear interaction cross sections for heavy projectiles (Z > or = 2) in targets of liquid H2, He and heavier materials. Such cross sections directly affect calculations of galactic and solar cosmic ray transport through matter and are needed for accurate radiation hazard assessment. To date, the collaboration has obtained data using the LBL Bevalac HISS facility with 20 projectiles from 4He to 58Ni in the energy range 393-910 MeV/nucleon. Preliminary results from the analysis of these data are presented here and compared to other measurements and to cross section prediction formulae.