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In this paper, a multiphase Lattice Boltzmann approach is adopted to directly simulate flow conditions that lead to the inception of cavitation in an orifice. Different values of fluid surface tension are considered, which play a dramatic role in the evolution of vapour cavity, as well as different inlet velocities at the computational domain boundary. The results of the flow simulations in terms of density and velocity magnitude fields are examined, with special focus on the components of the stress tensor inside the cavitating region: a comparison with cavitation inception criteria known form literature is proposed, highlighting the good agreement between our direct numerical simulations and theoretical predictions.