  In this work we review the classification of geodesics of massive test
particles in the gravitational background of the black hole solutions of
Einstein-Born-Infeld spacetime. Even though some features are quite similar to
those of Reissner-Nordstr\"{o}m spacetime there are also important differences,
particularly those related to the effective potential governing the geodesic
motion. Explicit solutions involving Weierstrass functions are given for a pair
of specific scenarios.
