The buckling of steel pipe piles during installation is numerically studied. Generally, numerical simulation of installation processes is challenging due to large soil deformations. However, by using advanced numerical approaches like Multi-Material Arbitrary Lagrangian-Eulerian (MMALE), such difficulties are mitigated. The Mohr-Coulomb and an elastic-perfectly plastic material model is used for the soil and pile respectively. The pile buckling behavior is verified using analytical solutions. Furthermore, the model is validated by an experiment where a pipe pile is driven into sand using vibratory loading. Several case scenarios, including the effects of heterogeneity in the soil and three imperfection modes (ovality, out-of-straightness, flatness) on the pile buckling are investigated. The numerical model agrees well with the experimental measurements. As a conclusion, when buckling starts, the penetration rate of the pile decreases compared to the non-buckled pile since less energy is dedicated to pile penetration given that it is spent mainly on buckling.