The ASME Boiler and Pressure Vessel Code Section XI prescribes the stress intensity factor solutions at the surface and deepest points for a semi-elliptical crack. The ASME Code Section XI, however, provides no solutions for a crack with a large aspect ratio, that is a crack in which the crack depth a is larger than the half-length c. The difficulty in treating the crack with a large aspect ratio relates to the position of the maximum stress intensity factor, which appears at neither the surface point nor the deepest point. In this paper, we investigate the influence of the stress intensity factor at the maximum point for circumferential and axial inside surface cracks with a large aspect ratio in a cylinder. First, we obtain the influence coefficients Gi for the stress intensity factor at the surface point, the deepest point, and the maximum point by finite element analysis, and developed a series of closed-form Gi solutions. Three geometrical factors are considered as parameters affecting the influence coefficients Gi: aspect ratio (a/ℓ = 0.5, 1.0, 2.0, and 4.0), crack depth ratio (a/t = 0.01, 0.1, 0.2, 0.2, 0.4, 0.6, and 0.8), and radius to thickness ratio (Ri/t = 2, 5, 10, 20, 40, and 80). Finally, we propose methods for evaluating the stress intensity factor for a crack with a large aspect ratio in a manner that characterizes the influence of the solutions at the maximum point.