Unconstrained rotational movement of an inner vessel with respect to an outer vessel at one end of a cryogenic storage vessel increases stress in supports at an opposite end. A storage vessel for holding a cryogenic fluid comprises an inner vessel defining a cryogen space and having a longitudinal axis, and an outer vessel spaced apart from and surrounding the inner vessel, defining a thermally insulating space between the inner and outer vessels. A structure for supporting the inner vessel within the outer vessel at one end comprises an inner vessel support bracket connected with the inner vessel, an outer vessel support bracket connected with the outer vessel, and an elongated support extending between and mutually engaging the inner and outer support brackets to constrain radial and rotational movement of the inner vessel with respect to the outer vessel and to allow axial movement of the inner vessel with respect to the outer vessel along the longitudinal axis.