A hydrogen generator capable of operating in any orientation and having no moving parts includes a catalyst retaining structure. The catalyst retaining structure is disposed in a housing and serves to separate the housing into a fuel holding portion and a hydrogen chamber. The catalyst retaining structure also includes one or more pores, each pore being in communication with the fuel holding and hydrogen chambers. A catalyst, that promotes the generation of hydrogen gas upon contact with the fuel, is disposed within the pores. The fuel enters the pores and thereupon generates hydrogen gas which passes into the hydrogen chamber. Contact of the fuel with the catalyst in the pores may be controlled and the position of the fuel-hydrogen interface within the pore may be moved so as to regulate the generation of hydrogen. The catalyst retaining structure can take different forms, including one or more hollow elongated members or plates, and may further incorporate hydrophobic and/or hydrophilic membranes.