The impact force on an elbow induced by traveling isolated liquid slugs in a horizontal pipeline is studied. A literature review reveals that the force on the elbow is mainly due to momentum transfer in changing the fluid flow direction around the elbow. Therefore, to accurately calculate the magnitude and duration of the impact force, the slug arrival velocity at the elbow needs to be well predicted. The hydrodynamic behavior of the slug passing through the elbow needs to be properly modeled too. A combination of 1D and 2D models is used in this paper to analyze this problem. The 1D model is used to predict the slug motion in the horizontal pipeline. With the obtained slug arrival velocity, slug length, and driving air pressure as initial conditions, the 2D Euler equations are solved by the smoothed particle hydrodynamics (SPH) method to analyze the slug dynamics at the elbow. The 2D SPH solution matches experimental data and clearly demonstrates the occurrence of flow separation at the elbow, which is a typical effect of high Reynolds flows. Using the obtained flow contraction coefficient, an improved 1D model with nonlinear elbow resistance is proposed and solved by SPH. The 1D SPH results show the best fit with experimental data obtained so far.