Computational Fluid Dynamics (CFD) analysis for the flow of non-Newtonian and gas-non-Newtonian liquid through elbows is presented. The commercial software Fluent 6.3 has been used for the simulation. Laminar non-Newtonian pseudoplastic power law model has been used for the simulation of non-Newtonian liquid flow through elbows. For twophase flow Elurian-Elurian approach has been used for simulation. The CFD analysis have been tested from our previously published experimental results, Bandyopadhyay and Das (2007), Bandyopadhyay et al. (2000).