We study how grain shapes impact multiphase flow in porous media in the quasi-static regime. An extended pore-network model with consideration of menisci pinning at sharp edges of grains is presented. Our results show that the effective contact angle distribution during displacement widens as the grain becomes more angular, which consequently modifies the macroscopic fluid invasion morphology. By analyzing various characteristic metrics during displacement, including capillary pressure signal, Haines jump size distribution, and fractal dimension, our results highlight the profound influence of particle shape on the multiphase flow.