  In this work, a regular black string solution will be presented from the
method used by Simpson-Visser to regularize the Schwarzschild solution. As in
the Simpson-Visser work, in this new black string solution, it is possible to
represent both a regular black hole and a wormhole just by changing the value
of a parameter "$a$" used in its metric. Tensors and curvature invariants were
analyzed to verify the regularity of the solution, as well as the energy
conditions of the system. It was found that the null energy condition will
always be violated for the entire space. The analysis of the thermodynamic
properties of the regular black string was also carried out, in which the
modifications generated about the original solution of the black string, were
evaluated, specifically, the Hawking temperature, entropy, its thermal
capacity, and the Helmholtz free energy. Finally, we investigate the possible
stable or unstable circular orbits for photons and massive particles. The
results were compared with those of the non-regular black string, seeking to
make a parallel with the Simpson-Visser work.
