This paper presents a numerical study of creep crack growth in a compact tension specimen. The constitutive behaviour of steel is described by a power law creep model. A damage-based approach is used to predict the crack propagation rate. Elastic-plastic-creep analyses are performed to predict crack extension under plane stress and plane strain conditions. The same load is applied at three different temperatures, 320°C, 360°C and 400°C. In addition, three different loads are applied at the same temperature, 360°C. Two parameters, C* and Q* parameters, are applied to characterise creep crack growth (CCG) rate for comparison. When C* parameter is used for the characterisation of CCG rate, tail parts are observed in the early stage for all F.E. predictions, while for Q* parameters these are not appeared. The F.E. results indicate that under fully steady state da/dt-C* relationship is little dependent on temperatures, load and stress conditions, while under early stage of CCG da/dt-Q* relationship is little dependent on temperatures, load and stress conditions.