Large igneous provinces (LIPs) are often the surface expressions of mantle plume process. Intensive magma could occur in the continental crust when a mantle plume penetrates the Moho. How magmas migrate in the crust, forming LIPs, remains debated. In this study, we employ 2D thermo‐mechanical numerical modelling to study the dynamics of magma intrusion and migration within the continental crust affected by a mantle plume. Our results suggest that (1) lateral magma migration dominates crustal deformation, promoting the possible formation of metamorphic core complexes; (2) two distinct crustal deformation modes are recognized regarding the presence or absence of crustal break‐up, affected by whether a significant vertical magma migration occurs; (3) the crustal thickness, Moho temperature and the length of the preset weak crust–mantle decoupling zone are the three key parameters controlling crustal magma migration. This study highlights the importance of lateral magma migration in the lower crust and provides physical mechanisms for the interpretation of magma migration under LIPs.