A number of surface cracks with large aspect ratio have been detected in components of nuclear power plants (NPPs) in recent years. The depths of these cracks are even larger than the half of crack lengths. When a crack is detected during in-service inspections, methods provided in ASME Boiler and Pressure Vessel Code Section XI or JSME Rules on fitness-for-service for NPPs can be used to assess the structural integrity of cracked components. The solution of the stress intensity factor (SIF) is very important in the structural integrity assessment. However, in the current codes, the solutions of the SIF are provided for semi-elliptical surface cracks with a limitation of a/ℓ ≤ 0.5, where a is the crack depth, and ℓ is the crack length. In this study, the solutions of the SIF were calculated using finite element analysis (FEA) with quadratic hexahedron elements for semi-elliptical surface cracks with large aspect ratio in plates. The crack dimensions were focused on the range of a/ℓ = 0.5–4.0 and a/t = 0.0–0.8, where t is the wall thickness. Solutions were provided at both the deepest and the surface points of the surface cracks. Furthermore, some of solutions were compared with the available existing results as well as with solutions obtained using FEA with quadratic tetrahedral elements and the virtual crack closure-integral method (VCCM). Finally, it was concluded that the solutions proposed in this paper are applicable in engineering applications.