  In this paper, we study the existence of (quasi)bound states in two spacetime
geometries describing Schwarzschild and Reissner-Nordstr\"om black holes. For
obtaining this type of states we search for discrete quantum modes of the
massive Dirac equation in the two geometries. After imposing the quantization
condition, an analytical expression for the energy of the ground states is
derived. The energy of higher states is then obtained numerically. For very
small values of the black hole mass $M$ we compare the energy of the
Reissner-Nordstr\"om black hole quasibound state with the Dirac-Coulomb energy
and we have found the two to be in good agreement.
