The shape variation of the laser beam is evidently observed in the laser powder bed fusion (LPBF) process because of changes in laser incidence angle and misalignment between the build plate and the laser focus plane. This issue is particularly relevant in large-scale LPBF systems where the laser beam needs to scan a large build area. However, most LPBF modeling studies assume vertical laser radiation. The heat transfer, melt pool, and solidification evolution due to the laser shape variation have not been well addressed and quantified. In the present study, the temperature distribution, melt pool geometry and flow dynamics are captured via numerical modelling, and the grain morphology is characterized under various laser incidence angles. The results show that the melt pool depth becomes shallower, and the width is near the beam size as the laser beam becomes more elongated. The beam shape variation can affect the liquid flow pattern with increasing incidence angle, resulting in a larger vortex at the front of the melt pool and a smaller vortex at the rear of the melt pool. The thermal gradient increases and the solidification rate decreases as the laser incident angle becomes larger. The present study enhances the understanding of multi-physics in the LPBF process.