Under overbalanced drilling co0ndition, a layer of particulates from drilling mud, called mud-cake or filter-cake, is often formed on the wellbore surface as the drilling fluid seeps through the surrounding geological formation. Mud-cake acts like a soft filter reducing the fluid pressure exerted on the wellbore surface by the fluid in the well. In this work, the safe mud weight window for wellbores with mud-cake is analytically derived by combining the long-term poroelastic wellbore stress solutions with steady-state flow solution for a two-layer cylindrical well. Parametric study on mud-cake permeability and thickness verifies that a wellbore with mud-cake transits smoothly from permeable wellbore to impermeable wellbore as the mud-cake accumulates. The new solution of breakdown pressure is also validated by a hydromechanical interaction numerical simulation.