Cap-rock integrity is of paramount importance during injection and subsequent long-term storage of CO2 in the subsurface. Preexisting (natural) and man-induced fractures in the cap rock represent potential flow paths out of the storage formation. In this study, a first-order semi-analytical model of flow through a vertical fracture penetrating cap rock is constructed taking the stressdependent fracture permeability into account. The model is then applied to study the effects of in-situ stress normal to fracture on the flow rate through the fracture. The flow rate increases nonlinearly with the reservoir pressure, which is due to a combined effect of nonlinear fracture deformation law and the cubic law governing the flow rate.