Résumé : A search for fully reconstructed Λ0b beauty baryons is performed using about 3 million Ζ decays collected with the DELPHI detector at LEP. The analysis relies on the combined use of the accurate tracking and of the hadron identification capabilities of DELPHI. A total of four events has been found, three in the Λ+cπ- channel and one in the Λ+ca-1 channel over a small background. The Λ0b beauty baryon mass is measured to be (5668 ± 16 (stat.) ± 8 (syst.)) MeV/c2.