Among other factors, thrust force, feed rate, twist drill bit chisel edge and point angle are the principal factors responsible for delamination drilling-induced damage during thermomechanical deformation. Hence, in this paper, an analytical thermo-mechanical model is proposed to predict critical feed rate and critical thrust force at the onset of delamination crack on CFRP composite cross-ply laminates, using the principle of linear elastic fracture mechanics (LEFM), laminated classical plate theory, cutting mechanics and energy conservation theory. The delamination zone (crack opening Mode I) is modelled as an elliptical plate. The advantages of this proposed model over the existing models in literature are that the influence of drill geometry (chisel edge and point angle) on push-out delamination are incorporated, and mixed loads condition are considered. The forces on chisel edges and cutting lips are modelled as a concentrated (point) and uniformly distributed loads, resulting into a better prediction. The model is validated with models in the literature and the results obtained show the flexibility of the proposed model to imitate the results of existing models.