Liquid slug flow driven by pressurized air in an inclined pipe with a downstream elbow is investigated numerically. As the liquid slug hits the elbow, the impact pressure and the associated force generated at the elbow may damage pipe supports as well as the pipe itself. It is essential for the design engineers of pipeline systems to accurately predict the pressure trace during the impact for safe operation. The slug arrival velocity and slug length (i.e., mass) at the elbow directly affect that pressure. In order to calculate these slug parameters just before the impact, an improved one-dimensional (1D) model proposed in the literature is used. At the elbow, pressure variation with respect to time is calculated by a recently developed computer code which uses a two-dimensional (2D) smoothed particle hydrodynamics (SPH) method. In the numerical setup, two representative initial slug lengths, one for short slugs and one for long slugs, and three different initial air tank pressures are used. The obtained numerical data are validated with available experimental results. For both short and long slugs, calculated peak pressures show great agreement with measured peak pressures.