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The airlift pump has the advantages of simple structure, strong reliability, convenient maintenance and low cost in the fields of deep seawater upwelling and seabed mining. This paper focuses on numerical analyses of steady air–water–solid three-phase flow as well as water–solid two-phase flow in the airlift pump based on one-dimensional multi-fluid model. The depth distributions of 8 physical quantities such as volumetric fractions and axial velocities of all phases, air density and pressure are calculated by solving the governing equations or by integrating the vector form of nonhomogeneous ordinary differential equations for three-phase flow interval and two-phase one, respectively. Upon successful verification of the present numerical model through a comparison with antecedent experimental results in case of a vertical pipe with length of 7.86 m, the model is extended to the case of seabed mining in water depth of 2000 m. The effects of the submerged depth of air–liquid–solid mixer, the diameter of solid particle and its density are considered. • The steady air–water–solid three-phase flow as well as water–solid two-phase flow in the airlift pump are considered by using one-dimensional multi-fluid model. • The depth distributions of 8 physical quantities such as volumetric fractions and axial velocities of all phases, air density and pressure are calculated by solving the governing equations for three-phase flow interval and two-phase one, respectively. • The model is extended to the case of seabed mining with water depth of 2000 m. • The effects of the submerged depth of air–liquid–solid mixer, the diameter of solid particle and its density are considered. [ABSTRACT FROM AUTHOR]