The electrostatic interactions between two identical, sufficiently thin, charged disks in an electrolyte solution are investigated. The charged entities can assume an arbitrary orientation in space, and their surfaces are either at constant charge density or at constant potential, We show that if the sm face potential is low, the governing Poisson-Boltzmann equation (PBE) can be solved analytically for the former. A boundary collocation method is adopted to solve the PBE for the latter. The interaction energies of the system under consideration including the electrostatic repulsive energy and the van der Waals attractive energy are estimated. We found that for a fixed center-to-center distance between two disks these energies are at maximum if they are on the same plane and at minimum if they are in an opposite position. The difference between the maximal and the minimal electrical repulsion energies increase with kappa r(0) for both constant surface charge and constant surface potential, kappa and r(0) being, respectively, the reciprocal Debye length and the radius of a particle. That for the van der Waals attraction energy follows the same trend.