Pressure drop estimation across orifices for two-phase liquid-gas flow is essential to size valves and pipelines and decrease the probability of unsafe consequences or high costs in petroleum, chemical, and nuclear industries. While numerically modeling flow across orifices is a complex task, it can assess the effect of numerous orifice designs and operation parameters. In this paper, two-phase flow across orifices has been numerically modeled to investigate the effect of different fluid combinations and orifice geometries on pressure drop. The orifice is assumed to be located in a pipe with fully-developed upstream and downstream flow. Two liquid-gas fluid combinations, namely water-air, and gasoil liquid-gas mixture were investigated for different orifice to pipe area ratios ranging from 0.01 to 1 for the superficial velocity of 10 m/s. Volume of Fluid multiphase flow model along with k-epsilon turbulence model were used to estimate the pressure distribution of liquid-gas mixture along the pipe. The numerical model was validated for water-air with mean relative error less than 10.5%. As expected, a decrease in orifice to pipe area ratio resulted in larger pressure drops due to an increase in the contraction coefficients of the orifice assembly. It was also found that water-air had larger pressure drops relative to gasoil mixture due to larger vortex formation downstream of orifices. In parallel, a mechanistic model to directly estimate the local two-phase pressure drop across orifices was developed. The gas void fraction was predicted using a correlation by Woldesemayat and Ghajar, and applied to separated two-phase flow undergoing contraction and expansion due to an orifice. The model results were validated for different orifices and velocities, with the overall relative error of less than 40%, which is acceptable due to the uncertainties associated with measuring experimental pressure drop. Comparison of the developed numerical and mechanistic model showed that the numerical model is able to achieve a higher accuracy, while the mechanistic model requires minimal computation.