Stress sensitivity phenomenon is an important property in low-permeability and tight reservoirs and has a large impact on the productivity of production wells, which is defined as the effect of effective stress on the reservoir parameters such as permeability, threshold pressure gradient, and rock compressibility change accordingly. Most of the previous works are focused on the effect of effective stress on permeability and threshold pressure gradient, while rock compressibility is critical of stress sensitivity but rarely noticed. A series of rock compressibility measurement experiments have been conducted, and the quantitative relationship between effective stress and rock compressibility is accurately described in this paper. In the experiment, the defects in previous experiments were eliminated by using a new-type core holder. The results show that as the effective stress increases, the rock compressibility becomes lower. Then, a stress sensitivity model that considers the effect of effective stress on rock compressibility is established due to the experimental results. The well performance of a vertical well estimated by this model shows when considering the effect of effective stress on the rock compressibility, the production rate and recovery factor are larger than those without considering it. Moreover, the effect of porosity and confining pressure on the productivity of a vertical well is also studied and discussed in this paper. The results show that the productivity of a vertical well decreases with the increase in overburden pressure, and increases with the increase in the porosity.