Radiation exposure estimates for crew members on the surface of Mars are made for solar particle event proton radiation environments comparable to the Carrington event of 1859. We assume that the proton energy distribution for this Carrington-type event is similar to that of the Band Function fit of the February 1956 event. In this work we use the BRYNTRN radiation transport code, originally developed at NASA Langley Research Center. The Computerized Anatomical Male and Female human geometry models were utilized to estimate exposures for polyethylene shield areal densities similar to those provided by a spacesuit, a surface lander, and a permanent habitat located at various altitudes in the Mars atmosphere. Comparisons of the predicted organ exposures are made with previously reported values obtained for aluminum shielding and current NASA Permissible Exposure Limits (PELs).