Abstarct: One of the most important problems in the design of engineering structures is to prevent the structure from breaking due to the stress created in the areas of geometric discontinuity. Usually, there are geometric defects in the form of the holes in the thin plates of parts and industrial structures. When these plates are exposed to tensile or thermal loads, the strong local stresses around the holes reduce the load bearing capacity of the structure. On the other hand, crack germination in the place of stress concentration is very common in engineering parts. Therefore, it is very important to investigate this phenomenon and deal with the growth of cracks and prevent accidents. One of the common damages in these materials is the creation of cracks in the places where stress is concentrated, including holes. One of the important parameters in investigating crack behavior is stress intensity factor. With the help of analytical method and using the relationships in fracture mechanics, stress intensity factor are obtained for a specific geometry. The purpose of this thesis is to determine the stress intensity factor in cracks emanating from cicular hole in orthotropic materials under tensile load and uniform heat flux in the distance. By using Moshkhalishvili's analytical method and finding the mapping function, the crack behavior emanating from the circular hole is analyzed and the stress intensity factors are calculated. To obtain the results with high accuracy, the mapping function is expanded with the sum of fractional terms.