Geometry and size effects on the crack growth resistance curves in CT-specimens of a low and high strength material are numerically investigated. The fracture process is controlled by experimentally determined critical values of the crack tip opening displacement (CTODi) for crack growth initiation and the crack tip opening angle (CTOAc) for stable crack growth. The results show that for the low and the high strength material the geometry and size effects are different. This is mainly due to the fact that the load vs. load line displacement records are basically different for the two materials which results from the large difference in the scaled fracture toughness parameters, CTODI/¢0 and CTOAc/¢o, of the two materials.