A mathematical expression is derived for computing dimensions of a liquid helium cryostat of specified performance characteristics. Use is made of a finite difference summation scheme applied to a simple thermomechanical model, usingTas the independent variable, for a liquid evaporating in a container with good exchange to the walls. The scheme thus takes into account the heat capacity of the gas between the boiling point and the upper cryostat temperature. The results obtained are compatible with the actual performance of cryostats in operation.