Fibre-reinforced concrete is the concrete with addition of short fibres targeting the improvement of the propriety of this material. Its durability is basely connected with the long-term dynamic loading. The main characteristic in that case are the critical stresses. The object of this article is steel fibre reinforced concrete (SFRC). For both materials (concrete and SFRC) are also different levels of critical stresses: initiation σi and critical σcr. Test findings during compression of concrete samples with and without fibre addition by means of acoustic and classical methods is presented. Three kinds of samples are assumed: BZ1 (1% fibres), BZ3 (3% fibres) and BZS (without fibre). In the case of concretes from groups BZ1 and BZ3, the level of initiation stresses was not found. The process of fibre-reinforced concrete compression has a two-stage character, instead of the process for witness concrete destroying is three-stages. It can be stated that the addition of steel fibres has the influence on σ-ɛ relationship for concretes in compression, and the level of critical stresses σcr increases together with the height of the quantity of steel-fibres added to the concrete-mixture. During compression the presence of dispersed reinforcement in concrete influences the propagation of cracks.