In the paper short glass and carbon fiber micro-mechanics in concrete matrix is under consideration. In present work was performed pull-out 3D numerical modeling. Numerical results were compared with realized experiments for single and few (fibre bundle) AR glass and carbon fibers pulling out of concrete matrix. Investigated were one fiber pull-out dynamics as well micro-stresses in the material. During performed single fiber pull out experiments were established such process mains steps: a) fiber and matrix elastic deformation with perfect bond between fiber and matrix; b) cylindrical delamination crack growth in material between fiber and concrete matrix; c) fiber break in concrete, after what free fiber end with friction is pulling out of matrix. Numerical model based on FEM were elaborated for all three failure steps. Numerical simulations were established mechanical background for such failure phenomena. Were established main load bearing and failure mechanism for short glass and carbon fiber concrete composites – single fiber pull out with simultaneous fiber failure.