In recent years, developments in the oil and gas industry have evolved significantly in advancing the mechanical systems technology to perform hydraulic fracturing. However, further developments will require an in-depth understanding of the impacts of fracture spacing, stress anisotropy, and reservoir characterization. In order to develop a comprehensive and robust completion design for hydraulic fracturing from multi-lateral wellbores with closely spaced fractures, it is important to consider stress shadowing effects. In this work the Cohesive Segments Method is combined with the Phantom Node Method, a combination termed CPNM. This is capable of not only simulating non-planar hydraulic fracture propagation with an unpredictable path, but also simulating the emergence of multiple cohesive cracks within a porous medium. This paper focuses on the “Modified Zipper-Frac” (MZF) design, which has been introduced to design the clusters from multi-lateral wells with the aim of increasing the fracture complexity. Validation of the numerical technique has been performed by comparing the solution for an individual hydraulic fracture with a Khristianovic-Geertsma-de Klerk (KGD) solution. In addition, a study of the development of double fractures has been conducted in the presence of stress shadowing to verify the simulation results. Taking the stress shadowing effects into account, a large number of numerical simulations are conducted using CPNM to investigate the stress anisotropy as well as the in-plane shear stress in the area between the two wells. The main contribution of this work is the detailed investigation of the effects of stress shadowing as a function of the fracture spacing on the horizontal stress contrast, direction of maximum local stress, leak-off flow rate, in-plane shear stress, and pore pressure of the formation.