  In this paper, we study the geodesic motion in spherically symmetric
electro-vacuum Euclidean solutions of the Einstein equation. There are two
kinds of such solutions: the Euclidean Reissner-Nordstr\"{o}m (ERN) metrics,
and the Bertotti-Robinson-like (BR) metrics, the latter having constant
Kretschmann scalar. First, we derive the motion equations for the ERN spacetime
and we generalize the results of Battista-Esposito, showing that all orbits in
as ERN spacetime are unbounded if and only if it has an event horizon. We also
obtain the Weierstrass form of the polar radial motion, providing an efficient
tool for numerical computations. We then study the angular deflection of orbits
in the Euclidean Schwarzschild spacetime which, in contrast to the Lorentzian
background, can be either positive or negative. We observe the presence of a
null and a maximal deflection rings for particles with velocity at infinity
$v>1$ and we give approximate values for their size when $v\gtrsim1$. For BR
spacetimes, we obtain analytic solutions for the radial motion in proper
length, involving (hyperbolic) trigonometric functions and we deduce that
orbits either exponentially go to the singularity or are periodic. Finally, we
apply the previous results and use algorithms related to Weierstrass' elliptic
functions to produce a Python code to plot orbits of the spacetimes ERN and BR,
and draw "shadows" of the first ones, as it was already done before for
classical black holes.
