Solutions of stress intensity factors for external and internal unpressurized and pressurized surface cracks in internally pressurized thick-walled reactor pressure vessels are determined directly by a three-dimensional displacement-hybrid finite element method. The finite element method is based on a rigorous modified variational principle of the total potential energy, with arbitrary element interior displacements, interelement boundary displacements and element boundary tractions as variables. Special crack front elements, developed using the hybrid displacement model, which contain the proper square root and inverse square root variations of displacements and stresses, are used in this analysis and the three stress intensity factors, KI, KII and KIII are solved directly along with the unknown nodal displacements. Stress intensity factor variations for pressurized and unpressurized semi-elliptical inner surface cracks in pressurized cylinders with crack aspect ratios of 0.2 and 1.0, crack depth to cylinder wall thickness ratios of 0.5 and 0.8 and outer to inner diameter ratios of 1.5 and 2.0, are presented. Also, for unpressurized outer surface cracks in pressurized cylinders, the solutions are presented for crack aspect ratios of 0.6 and 1.0, crack depth to cylinder wall thickness ratios of 0.4, 0.6 and 0.8, and outer to inner diameter ratio of 1.5.