This study establishes a three-dimensional cohesive model of multi-cluster hydraulic fracturing using finite element method (FEM). It fully considers the interaction between the interlayer and the reservoir and analyzes the key factors influencing fracture propagation. The results show that during the initial stage of hydraulic fracturing, the width of the edge fracture is greater than that of the mid fracture, while the situation is reversed for the fracture length. A larger cluster spacing leads to less interaction between fractures, while a greater number of clusters increases the interaction between fractures. With an increase in displacement, the lost fracturing fluid entering the formation enhances the interaction between fractures. An increase in elastic modulus results in a decrease in the width and height of edge fractures but an increase in their length, with little impact on mid fractures. As Poisson’s ratio increases, there is little change in the fracture morphology of edge fractures, while the width and height of mid fractures increase significantly. With an increase in permeability, the influx of fracturing fluid into the interlayer decreases, leading to a reduction in the interaction between fractures. Finally, the study analyzes and discusses the impact of these parameters on the SRV (stimulated reservoir volume) in both the reservoir and the interlayer. These findings provide new insights for hydraulic fracturing and contribute to improving its productivity.