Diagnostic fracture injection tests (DFIT) are used widely in the unconventional reservoirs to obtain formation properties. These properties can be crucial in optimizing primary and infill completions. The interpretation methods are assuming that pumping fluid would create a single planar fracture, however, perforation frictions and near wellbore stress concentration may accommodate initiation of fractures along the casing first (axial fractures). The possibility of the formation of an axial fracture increases in high injection rates and low differential stresses. In this study, we investigate the effect of the formation of an additional axial fracture on a DFIT test and its interpretation, using a fully coupled geomechanics and fluid flow model. We provide a model for the initiation and closure of axial and transverse fractures during the process. We also demonstrate that the estimate of the closure stress can be misleading when presence of an additional axial fracture is ignored. Finally, we discuss a potential method to determine the maximum horizontal stress under such circumstances. In fact, the variations in cement quality, cement type and its placement play roles in linking of adjacent perforations and form axial fractures, therefore it might be difficult to establish a safe perforation design to avoid initiation of axial fractures, but we can adjust our analysis to incorporate axial fractures effect.