The present work studies the possibility to decrease the formation of micro and nano cracks around short fibres in fibre-reinforced concrete (FRC) composite with the help of nano-reinforcement, which is carbon nanotubes, or micro reinforcement, which is carbon short fibres and nano-fillers. Tensile and bending strength of FRC depends on the spatial distribution of fibres inside a material, type of fibre and cement matrix, as well as an effective micromechanical work of each fibre while pulling out of the concrete matrix. Shrinkage stresses, acting in the matrix in the vicinity of a fibre, lead to the formation of micro-cracks. Such micro-cracks were observed experimentally and were investigated numerically performing broad modelling based on the finite element method (FEM). The investigation was focused on the micromechanical behaviour of a single steel fibre in a cement matrix. Numerical modelling results demonstrated a high level of shrinkage overstresses around steel fibres in concrete. The role of nano and micro admixtures, nanotubes, short carbon fibres as well as the role of water/cement ratio in a high performance concrete matrix, changing (increasing or decreasing) the friction force between the matrix and the steel fibre, were investigated experimentally by way of performing a single fibre pull-out tests. The high scatters of experimental results were obtained in performed pull-out tests. At the same time, for the same series of samples, a positive role of micro and nano admixtures and carbon nanotubes in the increase of pull-out force was recognised. © 2016 Vilnius Gediminas Technical University (VGTU) Press.