A human phantom torso experiment (PTE) has flown in space twice: once on Space Shuttle mission STS-91 (June 1998), and once on the International Space Station (ISS) (mid 2001). During these flights active and passive radiation dosimeters recorded space radiation exposures to five critical body organs (brain, thyroid, heart/lung, stomach, and colon) and to several surface (skin) locations. There are also plans to fly the PTE during the ISS 12A.1 mission with the Increment 8 crew (2003) and to fly a similar phantom torso experiment, called “Matroshka,” which will be mounted external to and on the ISS Service Module (2004). Recently, there has been interest expressed within the radiation biology community for measurements at specific red (and yellow) bone marrow sites in the human body. Current plans are to repeat the above organ site measurements, but also take space radiation measurements at several selected bone marrow sites in the forthcoming PTE and Matroshka flights. In this paper bone marrow computational exposures are presented for 52 identified locations in the human body using a modified version of the Computerized Anatomical Male (CAM) model. A “typical” ISS orbit of 385-km altitude and 51.6-deg inclination is used during a period of solar maximum. These results can provide utility to the experimenters, first, by establishing a pre-mission baseline threshold and exposure range, and second, as a post-flight comparison with their measurements, with the particle environment models, and with the spacecraft and human shielding models.