This paper deals with the influence of initial crack-tip shape, plastic compressibility and material or strain softening on near-tip stress-strain fields for mode I crack when subjected to fatigue loading with an overload event under plane strain and small scale yielding conditions. A finite strain elastic-viscoplastic constitutive equation with a hardening-softening- -hardening hardness function is taken up for simulation. For comparison, a bilinear hardening hardness function is also considered. It has been observed that the near-tip crack opening stress yy, crack growth stress xx, and hydrostatic stresses are noticeably controlled by the initial crack tip shape, plastic compressibility, material softening as well as the overload event. The distribution pattern of different stresses for a plastically compressible hardening- -softening-hardening solid appears to be very unusual and advantageous as compared to those of traditional materials. Therefore, the present numerical results may guide material scientists/engineers to understand the near-tip stress-strain fields and growth of a crack in a better way for plastically compressible solids, and thus may help to develop new materials with improved properties.