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Viscoelastic contact interfaces can be found in various robotic components that are covered with a compliant surface (pad) such as anthropomorphic hands, biomimetic haptic/tactile sensors, prostheses, and orthoses. In all these cases, it is desirable to obtain thin and resistant pads with predetermined compliance and damping properties (e.g., mimicking the human skin and pulpy tissues). In order to overcome the limits of homogeneous layers of a soft viscoelastic material, which is commonly used in the aforementioned devices, this paper suggests the adoption of soft pads that are composed of a continuous external layer (skin) coupled with an internal layer having fluid-filled voids. The process to design the pad starts with the selection of a hyperelastic medium with proper tribological features, whose constitutive parameters are determined by numerically fitting nonlinear stress-strain curves under pure homogenous deformations. The optimization of the internal layer morphology is then achieved through nonlinear finite element analysis (FEA) that provides an estimate of hardness and friction influence on the pad static compliance. Finally, the pad is filled with a viscous fluid that is chosen to modify time-dependent phenomena and to increase damping effects. The effectiveness of the procedure is proven by designing and modeling better-behaved artificial pads that mimic human-finger dynamic properties.