Deviations from conventional hydraulic fracturing simulators’ predictions are sometimes observed in the field and laboratory. This questions the basic assumptions adopted in linear hydraulic fracture mechanics (LHFM): a linear elastic solid and a simplified fluid flow in the fracture. Some rocks encountered in the domain of hydraulic fracturing show a strong non-linear behavior with the existence of a process zone, and fluid flow in small rough apertures also presents a departure from the Poiseuille law. By relating the solid non-linearity to the deviated fluid flow through the fracture roughness, we study the propagation of a radial fluid-driven fracture in quasi-brittle materials. We adopt a linear-softening cohesive zone model to simulate the non-linear behavior in the solid and introduces a friction factor to characterize the deviated fluid flow. We investigate the interplay between the fluid front and the process zone and verify that the solid non-linearity will impact the growth of hydraulic fractures through the fracture roughness by decreasing the permeability of the fracture tip. Fluid driven fracture propagation in quasi-brittle materials shows a similar behavior as in linear elastic solid under the assumption of a zero fluid lag. The cohesive zone develops with time and reaches a stable value, which depends on the fluid viscosity. When considering a non-zero fluid lag, an interplay exists between the fluid front and process zone. Deviated fluid flow pushes the fluid away from the fracture tip and results in a larger fluid lag. We observe a localization of the pressure drop near the tip. Cohesive zone length will either be shortened or enlarged by the deviated lubrication, depending on whether the squeezing or bubbling effect is dominant. However, normal stress drives the fluid front to the tip, leading to a smaller fluid lag and higher net pressure. Cohesive length is shortened as a result of a strengthened suction effect in the lag region. Due to this interplay, more energy dissipation is expected during propagation.