Underbalanced drilling and managed pressure drilling with foam have been gained attention of the world oil companies due to its many benefits. The advantages of this method include oil and gas production during drilling, high-speed drilling, drill bit life increase, better cutting transfer and reduced formation damage. In this paper cutting handling by foam was investigated in which foam was assumed to be a homogeneous, single-phase, compressible and non-Newtonian fluid whose rheological properties can be well described by power law model. The assumptions and governing equations of transient two-fluid model were expressed in Euler-Euler coordinate for fluid-particle (foam-cuttings). The upstream method is used to discretizing the equations and the results of the numerical solution are reported in the form of pressure, speed, cutting concentration, quality and density of the foam logs along the well. The impact of back-pressure, ROP, injection rate of gas and liquid, shape and size of cuttings, water influx and oil production on cutting concentration and bottom-hole pressure have been investigated. With increasing parameters such as back-pressure, liquid and gas flow rate, size of the cuttings and ROP, bottom hole pressure and cutting concentration increases. Cutting concentration decreases with increasing liquid and gas flow rate and increases by increasing back-pressure, cutting size and ROP. For validating, the results of the numerical solution are compared with field data obtained from well FR-1 located in the Santa Catarina state of Brazil which show about 16.5 percent errors.