In this work primary classification of the fastening systems according to the way of installation is given. The first group refers to the cast-in-place systems which are positioned before casting the concrete and the second group to the post-installed systems that are subsequently installed in hardened concrete. The focus of the work is given on the anchor channels which belong to the first group of fastening systems. First of all, the basic components of the anchor channel are described, as well as the installation procedure. In addition, concrete as a basic fastening material was briefly analyzed. Further, possible ways of loading of anchor channels are described, i.e. tension loads, shear loads or their combination. For each loading mode, the possible forms of bearing failure of anchor channels are shown, and the forms of bearing failure due to the action of shear load perpendicular to the longitudinal axis of the anchor channel are discussed in detail. The main goal of this paper is to analyze the load-bearing capacity of anchor channels in a non-cracked concrete element. A numerical analysis of the bearing capacity of anchor channels for two concrete slabs of different thicknesses according experiments available in the literature is performed by using two programs MASA and Femap. Based on the obtained results, a comparison of numerical and experimental results as well as the influence of concrete slab thickness on the load-bearing capacity of anchor channels is given.