The decays Λ b 0  → ψ(2S)pK− and Λ b 0  → J/ψπ + π −pK− are observed in a data sample corresponding to an integrated luminosity of 3 fb−1, collected in proton-proton collisions at 7 and 8 TeV centre-of-mass energies by the LHCb detector. The ψ(2S) mesons are reconstructed through the decay modes ψ(2S) → μ+μ− and ψ(2S) → J/ψπ + π −. The branching fractions relative to that of Λ b 0  → J/ψpK− are measured to be B(Λ0b→ψ(2S)pK−)B(Λ0b→J/ψpK−)=(20.70±0.76±0.46±0.37)×10−2, B(Λb0→ψ(2S)pK−)B(Λb0→J/ψpK−)=(20.70±0.76±0.46±0.37)×10−2, where the first uncertainties are statistical, the second are systematic and the third is related to the knowledge of J/ψ and ψ(2S) branching fractions. The mass of the Λ b 0 baryon is measured to be M(Λ0b)=5619.65±0.17±0.17 MeV/c2, M(Λb0)=5619.65±0.17±0.17 MeV/c2, where the uncertainties are statistical and systematic.