i think you mean "what are the internal reactions ?" ...
start with Roark, you've got 6 flat plates, bending under pressure, with in-plane bi-axial tension loads (the reactions from the adjacent faces). At 100 psi, i suspect that very quickly the deflection of the panels will make this a large displacement problem, with the faces reacting the applied pressure as a membrane (like a balloon, in-plane tension) rather than as a plate in bending.
then ther's the question of fixity of the edges.