Space radiation measurements were made on the International Space Station (ISS) with the Bulgarian Liulin-E094 instrument, which contains 4 Mobile Dosimetry Units (MDU), and the NASA ) during the time period May 11–July 26, 2001. In the time span 11–27 May 2001 four MDUs were placed at fixed locations: one unit (MDU #1) in the ISS “Unity” Node-1 and three (MDU #2–#4) units were located in the US Laboratory module. The MDTissue Equivalent Proportional Counter (TEPCU #2 and the TEPC were located in the US Laboratory module Human Research Facility (rack #1, port side). In this paper we discuss the flight observed asymmetries in different detectors on the ascending and descending parts of the ISS orbits. The differences are described by the shielding differences generated by different geometry between the predominating eastward drifting protons and the orientation and placement of the MDUs within the ISS. Shielding distributions were generated for the combined ISS and detector shielding models. The AP8MAX and AE8MAX trapped radiation models were used to compute the daily absorbed dose for the five detectors and are compared with the flight measurements. In addition, the trapped proton incident spectra inside of ISS were calculated using calibration curve of MDU obtained during the tests with protons at the Louvain-la-Neuve cyclotron facility. The energy of incident spectra maximums were analyzed against L value for the individual passes through the South Atlantic Anomaly.