Hydraulic fracturing is an extensively valuable stimulation method in oil and gas wells, which are no more producing efficiently, to improve the recovery of hydrocarbon from the reservoirs. The challenge of fracture initiation pressure and near-wellbore fracture propagation is a complex problem especially in deviated and cased perforated holes. In this paper a computer model is developed for estimating the initiation pressure as well as the orientation geometry of the fracture in the perforations around the borehole. Deviated well drilling techniques are used commonly all over the world to develop the reservoirs which are not well produced by vertical wellbores. Most of such wells are perforated after they have been cased and cemented. The existence of the casing along with the cement properties, considerably influence the stress distribution around the wellbore. In this model analytical equations are applied along with the numerical methods to analyze the stress profile around a cased cemented borehole with arbitrary inclination and azimuth. In addition, new analytical formulas are derived and applied to simulate the stress profile around the perforations, taking account of cement sheath and formation mechanical properties as well as perforation gun orientation. Results of this model are presented using common parameters at different in situ stress regimes, cement and rock properties, and also perforation and well trajectory limits. Wellbore tensile zone, fracture initiation pressure, and investigating the micro-annulus creation are among the main outputs of this modeling. It is concluded that, optimum well inclination and azimuth in conjunction with perforation orientation as well as cement properties can be derived at various stress regimes. As a result lower fracture initiation pressure with better fracture orientation geometry in terms of linking up of small fractures and less fracture tortuosity can be achieved. The significance of this model is its ability in analyzing the stress profile along the perforations tunnel and casing cement sheath, so more realistic fracture initiation pressure and near-wellbore fracture geometry would be anticipated.