A fiber bundle cartridge for a fiber membrane degassing system includes an inner sleeve including one or more perforations and a fiber bundle positioned radially outward from the inner sleeve. The fiber bundle has an annular shape defining a central bundle axis. The perforations of the inner sleeve define a plurality of inlets and/or outlets facing radially with respect to the central bundle axis. A fiber membrane degassing system includes a housing defining a cylindrical volume having at least one inlet and at least one outlet. The system includes at least one fiber within the cylindrical volume, where fluid flowing through the cylindrical volume from the at least one inlet to the at least one outlet flows perpendicular to a longitudinal dimension of the fiber. A method of degassing a liquid includes directing a liquid volume through a fiber bundle in a direction radial to a longitudinally extending bundle axis.