Hydraulic fracturing has been used for many years in order to stimulate the oil and gas wells for improving the reservoir production. Many investments are allocated for hydraulic fracturing all around the world to develop hydrocarbon resources. Most of them are done for cased holes which some of them do not significantly improve the hydrocarbon production. The main reason is improper fracture initiation and complex near-wellbore fracture geometry which is a challenging problem. In cased holes, the perforations are the only connection between the well and the reservoir, therefore the fracture initiates somewhere in the perforation. Understanding the stress distribution around the perforations is the key for analyzing the fracture initiation mechanism and thereby the near-wellbore fracture geometry. In this paper new analytical formulas are derived and applied along with numerical methods to simulate the stress profile around the perforations. Having analyzed the perforation stress distribution, it is possible to understand the mechanism of fracture initiation and consequently improving the near-wellbore fracture geometry. Results of this model are presented at some in-situ stress regimes, cement and rock properties, and also perforation and well parameters. It is concluded that, at any specific stress regime, there is an optimum well design and completion, and also perforation orientation, which leads to lower fracture initiation pressure as well as better fracture orientation geometry in terms of less near-wellbore fracture tortuosity. Therefore, better connection can be developed between the borehole and the reservoir formation. The importance of this model is its ability in analyzing the stress profile along the perforation tunnel, so more realistic fracture initiation pressure and fracture geometry can be estimated for better well completion and perforation design.