The effect of a normal H2 impurity upon the radial thermal expansion (Ar) of SWNT bundles has been investigated in the interval T = 2.2-27 K using the dilatometric method. It is found that H2 saturation of SWNT bundles causes a shift of the temperature interval of the negative thermal expansion towards lower (as compared to pure CNTs) temperatures and a sharp increase in the magnitude of (Ar) in the whole range of temperatures investigated. The low temperature desorption of H2 from a powder consisting of bundles of SWNTs, open and closed at the ends, has been investigated.