Visibility analysis is broadly used in milling and casting process planning and in coordinate measuring machine applications. However, standard visibility analysis (which involves determining visibility from a given viewpoint), cannot be applied directly to in-line cutting systems such as wire electrical discharge machines or hot wire foam cutters. The motivation of this paper is to accurately calculate the tangent visibility for objects represented by polygonal surfaces. In this paper we define a new type of visibility - tangent visibility. We develop an algorithm to calculate the global tangent visibility for in-line cutting systems, and several models are tested to verify its accuracy. Several polyhedral models are tested to verify the correctness of the tangent visibility algorithm; and the complexity of the algorithm is also discussed.