Two-parameter descriptions of the crack tip stress fields in elastic-plastic materials are discussed in detail. It is shown analytically that the two-term asymptotic expansions for the near-tip stresses developed by Li and Wang  and Sharma and Aravas  can be represented in an alternative form in which the leading HRR-term can be replaced by the standard small-scale-yielding solution (with T = 0). A two-parameter characterization of the plane strain elastoplastic crack tip fields of edge-cracked geometries is presented. Detailed finite element calculations of edge-cracked bars loaded in tension (SENT) are carried out for different values of the crack length (a) to specimen width (W) ratio. The crack tip fields are characterized in terms of J-integral and the magnitude Q1 of the second term of the elastoplastic crack tip asymptotic solution. Comparison are made with the alternative pairs of parameters (J, T) and (J, Q) that have been suggested by Hancock and co-workers ([21, 22, 23, 24]) and O'Dowd and Shih ([7, 8]) respectively, where T is the so-called elastic-T-stress and Q is a measure of the crack tip stress triaxiality. Plane strain creep solutions are also obtained for a shallow-cracked SENT specimen with a/W = 0.05. It is found that, whereas the region of dominance of the HRR-like term is essentially zero, a two-term asymptotic expansion similar to that used in elastic-plastic materials provides an accurate description of the spatial and temporal variations of the crack tip stresses of the creeping solid.