The present work compares the micromechanical approach and the continuum approach for modeling microcracked continuum. The first approach considers a distribution of microscopic cells including contacting lips (discontinuity of matter), and the second approach considers a distribution of singularity in a continuum (discontinuity of fields). The main difference in these two methods is due to the choice of internal variables capturing the interstitial dissipation: torsion and curvature of the affine connection in the continuum approach and jump of velocity and temperature across the cracks for the micromechanical approach. The continuum approach involves more details than the micromechanical approach due to the accounting for both the translations and rotations of contacting lips.