Electron tomograms have revealed that in normal mitochondria crista membrane self-assembles into a complex structure that contains both flat lamellar and tubular components connected to the inner boundary membrane through crista junctions. This structure with one single matrix compartment is believed to be essential to the proper functioning of mitochondria. We present a model from which the observed morphology of the inner mitochondrial membrane can be inferred as minimizing the system's free energy. Using the observed geometrical features, we then predict thermodynamic properties of the system; such properties include surface tension, pressure difference and stabilizing tensile forces which are not directly observable. Free energy of the membrane has contributions from resistance of the membrane to bending, surface tension and osmotic pressure difference across the membrane and assumes mechanical forces acting on the membrane that we believe to be exerted by mechano-enzyme protein scaffolds. To that end, a set of geometric measurements from the structural features of mitochondria in Hela cells and mouse embryonic fibroblasts were obtained. Structural features were measured from 3D electron tomograms of mitochondria. These tomograms were obtained by collecting dual-axis tilt series of 300 nm sections of mitochondria around two orthogonal axes, aligning the projection images of each tilt series to a common origin and applying a filtered backprojection algorithm to the aligned tilt series to calculate the tomograms of each axis. The two tomograms are aligned to each other with general 3-D linear transformations to correct for distortions between the tomograms. Full tomograms were obtained by joining the reconstructions of up to four serial 300 nm sections. From the measured structural features, measurements of other features of crista membranes are extrapolated computationally. The free energy model combined with the geometric measurements predicts that a stress-induced coexistence of tubular and flat lamellar phases are stabilized by tensile forces of the order of 20 pN, comparable to those typical of dynamin protein scaffolds and motor proteins. It also predicts the pressure differences of -0.037 ± 0.008atm (pressure higher in the matrix) and surface tension equal to 0.077 ± 0.02 pN nm.