In this article, we study the Gauss map of generalized slant cylindrical surfaces (GSCS''s) in the 3-dimensional Euclidean space E^3. Surfaces of revolution, cylindrical surfaces and tubes along a plane curve are special cases of GSCS''s. Our main results state that the only GSCS''s with Gauss map G satisfying ?G = AG for some 3 ? 3 matrix A are the planes, the spheres and the circular cylinders.