In most of the polycrystalline materials, cavity nucleation, growth and coalescence at grain boundaries (Gb) ahead of a crack tip are regarded as major aspects of micromechanisms of creep crack growth. Therefore, the modelling of creep crack growth requires proper understanding of the crack tip stress field and the process of cavity growth in a given local stress state. The stress field ahead of a crack is usually affected by the presence of cavities, which in turn influences the kinetics of the cavitation. Even though the stress analysis and cavity growth are not separable problems, the analytic solution of the stress field in which the cavitation effect is incorporated can only be found in a limited number of cases. In this study, the analytic solution of the stress field for the steadily growing crack with Gb cavitation was obtained by solving the second kind Fredholm type singular integral equation. The macroscopic material behavior was assumed to be elastic, thus, the original stress distribution was determined by the K field, i.e. K/$\sqrt{2\pi{r}}$, of linear elastic fracture mechanics. The effect of stress relaxation by local cavitation was calculated using the infinitesimally distributed dislocation model. Diffusive cavity growth model by Trinkaus and Ullmaier was used for two types of sintering stress distribution, which were assumed to be constant and variable according to the cavity size, respectively. As a result, the singularity of resultant stress distribution at the crack tip was relaxed by the parameter $\theta$ due to Gb cavitation, i.e. the singularity changed from $r^{-1/2}\;\;\mbox{to}\;\;^{-1/2+\theta}$.The relaxation parameter $\theta$, which ranged between O and 1/2, was determined by the material properties, average inter-cavity spacing and crack velocity. At the region near the end of cavitating zone, the stress increased in order to meet the force equilibrium condition of the total system, which caused the resultant cavitating zone size to expand as a function of $\theta$. The ratio of the cavitating zone size in the relaxed stress field to that in the original K field became a maximum when $\theta$ is 1/2. Also the analytic expression was obtained for the relation between crack velocity and applied load parameter K. The crack velocity was proportional to K$^2$ when the applied load K was so high that the relaxation effect was negligible. However, as the value of K decreased, there appeared the threshold value of $K_{th}$ such that crack growth was no longer possible when $K \le K_{th}$. At the threshold of K, the relaxation parameter $\theta$ is 1/2 so that the stress was fully relaxed to the sintering stress level throughout the cavitating region. In case of cavity size dependent sintering stress condition, which was more realistic, the stress distribution at the crack tip had the same singularity with that in the case of constant sintering stress, irrespective of the assumed sintering stress forms. At the other side of the cavitating zone, however, the stress profile was quite dependent on the sintering stress form with the maximum peak value near at the outer boundary of cavitating region. Especially, when the applied load K was near the $K_{th}$, the relation between cavitating zone size and applied load K was reversed, i.e. even though the load K decreased, the size of cavitating extended until K reached $K_{th}$.
