In developing shale oil reservoirs, the evolution of induced stress in the reservoir is complex, affecting the operation of adjacent wells. In this paper, the longitudinal sand-shale interbed shale oil reservoir is taken as the research object, and a stress-sensitive model is established. A prediction model for the evolution of induced stress in the fractured shale oil reservoir is proposed based on poroelasticity. This model preliminarily characterizes the dynamic evolution of in-situ induced stress within and between layers under the condition of longitudinal heterogeneity. Conclusions can be drawn from the simulation results: in the case of multi-layer co-production, the evolution of stress profiles at different locations near the horizontal well is different. The horizontal stress decreases between layers near the middle well and increases near the ends of the well. As production time increases, the amplitude of effective minimum horizontal principal stress and the stress deflection angle in sandstone are greater than those in shale. After three years of production, the maximum alteration angle of the minimum horizontal principal stress in the sandstone layer reaches 79°. The model established in this paper provides the theoretical support for good arrangement and fracturing design of shale oil reservoirs.