In the present paper, a phenomenological one-dimensional model of a two-phase gas and liquid flow in a trickle bed reactor is developed. Based on some realistic assumptions specific to tickling flow regime, the original equations of continuity and momentum are reformulated in terms of liquid saturation and gas pressure equations. The computational method used is the finite volume technique combined with Godunov's method. It is shown that the pressure drops derived from the model solution are in good agreement with those measured in the same operating conditions and with previous literature results.