A two-dimensional mathematical model was studied for the transport of CO2 and H2S through hollow fiber membrane (HFM) contactors while using MEA (monoethanolamine) as the chemical absorber. The model considered non-wetted where the gas and the solvent liquid fill the membrane pores for counter current gas–liquid flow direction. There is an axial and radial diffusion in the tube, through the membrane and the shell. The model validation was on the physical and chemical absorption of CO2 using water and MEA, respectively. The percentage of removal of CO2 increased while increasing the absorbent velocity. As for H2S, low flow rate of amine was efficient in complete removal. The percentage removal of CO2 decreased while increasing gas velocity because of lower hold up time, whereas H2S removal did not change with increasing gas velocity at low gas velocities. However the effect is more obvious at high gas velocities.