Based on a set of constitutive relations developed for porous solids with rate-dependent pressure-sensitive matrices, the stress, strain and void volume fraction distributions are investigated near time crack tip with a finite root radius under mode I, plane strain, and small-scale yielding conditions. A rubber-modified epoxy is taken as our model. The rubber particles are taken as the void volume fraction from the view of stress-carrying capacity when the epoxy is subject to extensive plastic deformation. The set of constitutive relations for porous solids is based on a generalized Gurson yield criterion for porous solids with pressure-sensitive matrices. Time set of constitutive relations has been implemented into finite element code ABAQUS to investigate the near-tip field of a crack in porous solids. Our numerical results indicate that the plastic zones, the intense straining zones, and large void volume fraction contours are long and narrow ahead of a crack tip in porous solids with moderately large initial void volume fractions. The strain softening and subsequent hardening of the matrices also make these zones more concentrated ahead of the tip, As the initial void volume fraction or the pressure sensitivity of the matrices increases with a decrease of plastic dilatancy, these zones become more elongated ahead of the tip. The cavitation of the rubber particles in the rubber-modified epoxy is also considered via a stress-controlled void nucleation model. The numerical results for the rubber-modified epoxy based on the nucleation criterion shown that the shape and size of the intense straining and cavitation zones agree well with the corresponding experimental results.