—Coverage is a fundamental problem in Wireless Sensor Networks (WSNs). Existing studies on this topic focus on 2D ideal plane coverage and 3D full space coverage. In many real world applications, the 3D surface of a targeted Field of Interest is complex, however, existing studies do not provide promising results. In this paper, we propose a new coverage model called surface coverage. In surface coverage, the targeted Field of Interest is a surface in 3D space and sensors can be deployed only on the surface. We show that existing 2D plane coverage is merely a special case of surface coverage. Simulations point out that existing sensor deployment schemes for a 2D plane cannot be directly applied to surface coverage cases. In this paper, we target two problems assuming surface coverage to be true. One, under stochastic deployment, how many sensors are needed to reach a certain expected coverage ratio? Two, if sensor deployment can be planned, what is the optimal deployment strategy with...