Distribution of neutron equivalent dose both inside and outside the spherical phantom (experiment Matryeshka-R) was determined with the help of dedicated research equipment "Bubble-dosimeter". Equipment is built up from an automatic bubbles counter and 8 bubble detectors of neutrons with energy ranging from approximately 200 keV to 15 MeV. Measurements inside the ISS were made in several 7-day sessions in the period from April 2006 till October 2007 (ISS increments 13-15). According to the bubble detectors on the outside of the phantom, ambient neutron dose H*(10) was equal to 0.1 mSv/d or approximately 20% of the dose from charged particles inside the ISS. In the tissue-equivalent phantom, neutron dose was 1.2 +/- 0.2 times less as compared with the phantom surface which characterized the degree of dose attenuation in cosmonaut's body.