The motion of long bubbles into Newtonian and non-Newtonian fluids confined in horizontal circular tubes, rectangular channels, and square cross-sectional channels has been studied both theoretically and experimentally. Of particular interest is the determination of residual liquid film thickness on the walls. Isothermal experiments have been conducted to measure the displacement of the gas-liquid interface as a function of the applied pressure differential. The velocity of the interface and residual liquid film thickness have been determined for both Newtonian and non-Newtonian (shear thinning and viscoelastic) fluids. These experimental results are in good agreement with similar experimental studies conducted by other investigators. The experimental results indicate that the liquid film thickness of constant viscosity viscoelastic fluids (Boger fluids) deposited on the tube wall is thicker than that of comparable Newtonian fluids. A simple mathematical analysis was developed using a power-law model. The mathematical model successfully captures the gas-liquid dynamics for Newtonian and non-Newtonian fluid displacement in a tube and rectangular channel. The prediction of the liquid fraction deposited on the walls is in qualitative agreement with the experimental observations of previous investigators (Chem. Eng. Sci. 24 (1969) 471; A.I.Ch.E. 16 (1970) 925; Chem. Eng. Sci. 30 (1975) 379). The model gives similar results to a numerical solution (Polm. Eng. Sci. 35 (1995) 877) in which a constitutive equation containing a yield stress is used to model the non-Newtonian behavior. The model is used to determine the location and velocity of the advancing bubble front for the case of a power-law fluid. The results indicate that the gas-liquid interface advances more rapidly with decreasing values of the power-law index above a certain value of dimensionless time (t/t(b) approximate to 0.75).