An extension of a mathematical model for non-isothermal multiphase materials to consider the dissolution of air in liquid water and air mass sources during its desorption at lower water pressure is presented. The solid skeleton is assumed elasto-plastic; heat, water and air flows and water phase changes are taken into account. Physics of air dissolution and desaturation due to the air released from liquid water during cavitation in porous media are discussed. A numerical example where cavitation develops during shear band development in undrained water-saturated dense sands is solved with the developed model as discretized in space and time with the Finite Element Method.