The singularity near are-entrant corner of Oldroyd-B fluid has been studied in the literature, at least for re-entrant corner gamma = 270 degrees. It was shown that, except near, the walls, the flow develops singularities which are self-similar, very much like the Newtonian singularities. This paper considers the case of a general Oldroyd model and a general re-entrant corner. Under some assumptions on the coefficients of the Oldroyd model (which exclude the Oldroyd-A and Oldroyd-B models) it is shown that the singularity is a sum of a Newtonian singularity plus a lower order non-Newtonian singularity; the latter singularity is not a similarity solution, and, in particular, it is highly oscillatory near the downstream wall, in the vicinity of the corner.