We investigate the behavior of a model methane clathrate cage under high hydrostatic pressures. The methane clathrate cage consists of 20 water molecules forming 12 pentagonal faces, with a methane molecule positioned at the cage center. The clathrate compound is located inside a fullerene-type arrangement of 180 He atoms to simulate an isotropic pressure. Different pressures are simulated by decreasing the radius of the He array. The minimal energy of the total system for each configuration is calculated by using density functional theory. The variation of the energy with the volume of the imprisoned clathrate cage leads to the proposal of a (cold) equation of state in the pressure range [0,60] GPa. The elastic parameters of the state equation are found in agreement with equivalent quantities measured on clathrates in their sI conformation. Special attention is given to the distribution of the confined atoms and the eventual symmetry lost from the clathrate cage with the pressure, as the clathrate cage constitutes a basic structural unit of the crystal. Finally, the strengths and limitations of the model are discussed.