Collective cell migration is crucial in many biological processes such as wound healing, tissue morphogenesis, and tumor progression. The leading front of a collective migrating epithelial cell layer often destabilizes into multicellular finger-like protrusions, each of which is guided by a leader cell at the fingertip. Here, we develop a subcellular-element-based model of this fingering instability, which incorporates leader cells and other related properties of a monolayer of epithelial cells. Our model recovers multiple aspects of the dynamics, especially the traction force patterns and velocity fields, observed in experiments on Madin-Darby canine kidney cells. Our model predicts the necessity of the leader cell and its minimal functions for the formation and maintenance of a stable finger pattern. Meanwhile, our model allows for an analysis of the role of supracellular actin cable on the leading front, predicting that while this observed structure helps maintain the shape of the finger, it is not required in order to form a finger. In addition, we also study the driving instability in the context of continuum active fluid model, which justifies some of our assumptions in the computational approach. In particular, we show that in our model no finger protrusions would emerge in a phenotypically homogenous active fluid and hence the role of the leader cell and its followers are often critical.