We consider the Neumann problem outside a small neighborhood of a planar disk in the three-dimensional space. The surface of this neighborhood is assumed to be smooth, and its thickness is characterized by a small parameter e. A uniform asymptotic expansion of the solution of this problem with respect to e is constructed by the matching method. Since the problem turned out to be bisingular, an additional inner asymptotic expansion in the so-called stretched variables is constructed near the edge of the disk. A physical interpretation of the solution of this boundary value problem is the velocity potential of a laminar flow of an ideal fluid around a thin body, which is the neighborhood of the disk. It is assumed that this flow has unit velocity at a large distance from the disk, which is equivalent to the following condition for the potential: u(x1, x2, x3, e) = x3+O(r−2) as r → ∞, where r is the distance to the origin. The boundary condition of this problem is the impermeability of the surface of the body: ∂u/∂n = 0 at the boundary. After subtracting x3 from the solution u(x1, x2, x3, e), we get a boundary value problem for the potential ũ(x1, x2, x3, e) of the perturbed motion. Since the integral of the function ∂ũ/∂n over the surface of the body is zero, we have ũ(x1, x2, x3, e) = O(r−2) as r → ∞. Hence, all the coefficients of the outer asymptotic expansion with respect to e have the same behavior at infinity. However, these coefficients have growing singularities at the approach to the edge of the disk, which implies the bisingularity of the problem.