A numerical study of adhesive contact between rough surfaces with soft coating is presented using an elastic-plastic model of asperity contact deformation. The analysis considers the elastic and plastic deformation of both the coating and the substrate unlike the work available in literature where the coating is considered to be in pure plastic contact. The JKR (Johnson-Kendall-Roberts) adhesion model is used and the well-established adhesion indices (elastic and plastic adhesion indices) are utilized to consider the different conditions of varying load and material and surface properties of the substrate and the coating. Contact load and contact area are obtained as functions of mean separation between surfaces for different combinations of adhesion parameters, material properties and thickness of the coating. The effects of these parameters on contact behavior of coated surfaces are investigated. For thin coating and light loading, contact is strongly influenced by the existence of soft coating that increases the contact area due to plastic deformation of the coating.