Hydraulic fracturing (HF), as a stimulation technique in petroleum engineering, has made possible the oil production from reservoirs with very low permeability. The combination of horizontal drilling and multiple HF with various perforation angles has been widely used to stimulate oil reservoirs for economical productions. Despite the wide use of HF, there are still ambiguous aspects that require more investigation. Therefore, optimizing the geometry of the initial fractures using numerical methods is of high importance in a successful HF operation. Different geometrical parameters of the initial HF cracks including patterns, spacings, crack lengths, and perforation phase angles were modeled using the higher order displacement discontinuity method (HODDM) in horizontal and vertical oil wells. Several well-known issues in HF such as crack interference and crack arrest were observed in certain patterns of the HF cracks. Also the best possible arrangements of the HF cracks were determined for a better production. The results obtained were verified by the in-situ measurements existing in the literature. In addition, the best perforation phase angle in vertical wells was investigated and determined.