This paper is concerned with the study of singular integral operators associated with the Neumann problem for the bi-Laplacian in infinite sectors in the plane. The main goal is to explicitly describe the Mellin symbol of such singular integral operators for arbitrary apertures θ ∈ (0, 2π) and Poisson ratios η ∈ [−1, 1). The analysis carried out here uses Mellin transform techniques and properties of hypergeometric functions of gamma, beta, Ferrers and Gauss type. The explicit Mellin symbol formulas open the door to obtaining information on the range of integrability exponents p ∈ (1,∞) for which the Neumann problem for Δ2 is well-posed in this geometric setting.