Tank for storing cryogenic fluid, and in particular a two-phase mixture of liquid and of gas, comprising a first casing intended to contain the cryogenic fluid, at least one drawing-off pipe (5, 7) having an upstream end connected to the first casing and being configured to allow fluid contained in the first casing to be drawn off towards the outside of the tank, a circuit for filling the tank, the filling circuit comprising a first filling pipe having an upstream end intended to be connected to a fluid source and a downstream end connected to the lower portion of the first casing, the filling circuit comprising a second filling pipe having an upstream end intended to be connected to the fluid source and a downstream end connected to the upper portion of the first casing, the upstream ends of the first and second filling pipes being intended to be simultaneously connected to one and the same fluid source, the filling circuit comprising a set of one or more distribution valve(s) configured to allow the fluid originating from the fluid source to be distributed in the filling pipes (9, 10), the tank comprising a set of one or more sensor(s) measuring the pressure in the first casing, the set of one or more distribution valve (s) being configured to automatically regulate the pressure in the first casing to a predetermined pressure setpoint (Pc) during filling by ensuring automatic distribution of the flow of fluid originating from the source in the filling pipes (9, 10), as a function of the pressure setpoint (Pc) and of the pressure measured by the set of one or more sensor (s), characterized in that the set of one or more distribution valve(s) comprises a housing having a fluid inlet intended to be connected to the source, two outlets respectively connected to the two filling pipes (9, 10) and a translationally and/or rotationally movable distributor located in the housing and ensuring connection or non-connection of the inlet with the one or more outlets according to the position of the movable distributor and in that the set of one or more distribution valve(s) is configured to automatically interrupt any passage of fluid originating from the source towards the filling pipes (9, 10) when the pressure measured by the set of one or more sensor (s) is higher than a first determined safety threshold, and in that the set of one or more distribution valve(s) is a solely mechanical device comprising at least one valve that is actuated via a set of one or more return component(s), in particular one or more springs, and/or a solely pneumatic device comprising at least one valve that is actuated pneumatically, and/or the set of one or more distribution valve(s) being sensitive to the pressure measured by the set of one or more sensor (s) measuring the pressure in the first casing, the set of one or more distribution valve(s) having a single movable element closing or opening a passage for the fluid between the fluid source and the one or more filling pipes (9, 10), said movable element being moved into a plurality of positions according to the pressure difference between, on the one hand, a setting force corresponding to the predetermined pressure setpoint (Pc) and, on the other hand, the pressure measured by the set of one or more sensor(s).