Synchrotron X-ray diffraction has been used to investigate structure, stability, and transformation of the Pn3m bicontinuous cubic phase in the monoolein-water system under hydrostatic pressure. As a first result, it appears that the full-hydration properties of monoolein are strongly related to the pressure. Moreover, the experimental results show the occurrence of a Pn3m to Ia3d cubic phase transition when the mechanical pressure increases to 1-1.2 kbar, depending on the water concentration. The underlying mechanism for the phase transition has been then explored in searching for relationships between the structural parameters derived from the two cubic phases. The emerging picture is a change in the basic geometrical shape of the monoolein molecule during compression. Moreover, the analysis of the position of the pivotal surface indicates that the interface is bending and stretching simultaneously as a function of pressure. Because the lipid concentration is rather low and the external pressure increases the cell sizes, thus reducing the principal curvatures, a tentative analysis of the pressure effects on the energetics of these structures has been exploited. A simple theoretical model based on curvature elastic contributions has been used: calculations show that increasing the pressure the spontaneous curvature Ho of the monoolein tends to zero, whereas the ratio between the monolayer saddle splay modulus and the monolayer splay modulus k(G)/k increases td 1. Moreover, the curvature elastic energy appears to reduce progressively as a function of pressure, indicating that in these conditions, the curvature elasticity does not dominate the total free energy.