This paper is concerned with compliant haptic contact and deformation of soft objects. A human soft fingertip model is considered to act as the haptic interface and is brought into contact with and deforms a discrete surface. A nonlinear constitutive law is developed in predicting normal forces and, for the haptic display of surface texture, motions along the surface are also resisted at various rates by accounting for dynamic Lund-Grenoble (LuGre) frictional forces. For the soft fingertip to apply forces over an area larger than a point, normal and frictional forces are distributed around the soft fingertip contact location on the deforming surface. The distribution is realized based on a kernel smoothing function and by a nonlinear spring damper net around the contact point. Experiments conducted demonstrate the accuracy and effectiveness of our approach in real-time haptic rendering of a kidney surface. The resistive (interaction) forces are applied at the user fingertip bone edge. A 3-DoF parallel robotic manipulator equipped with a constraint based controller is used tor the implementation. By rendering forces both in lateral and normal directions, the designed haptic interface system allows the user to realistically feel both the geometrical and mechanical (nonlinear) properties of the deforming kidney.