The present invention relates to installations and methods for storing and restoring electrical energy comprising two, a first and a second, lagged chambers (1,2) containing porous refractory materials (11) through and between which a gas is circulated by causing the gas to circulate through two, a first and a second, compression / expansion sets (30, 40) interposed in the circuit of pipework (1c, 1d, 2c, 2d) between the upper ends (11, 21) and, respectively, lower ends (12, 22) of said first and second chambers, each compression / expansion set comprising a piston (30a, 40a) to which there is imparted a translational movement in a cylinder (30b, 40b), each set operating in a different mode, either in compression mode or in expansion mode, one of the two compression / expansion sets receiving a gas at a higher temperature than the other set such that, in compression mode, it is operated by an electric motor (41) which consumes electrical energy that is to be stored E1, and in thermodynamic engine mode it operates an electric generator (52) able to restore electrical energy (ER). The electrical energy is stored in the form of heat in masses of refractory products, and this stored thermal potential energy is restored in the form of electrical energy.