Significant stress concentrations occur at the interface of floor slabs and columns in widely used monolithic reinforced concrete beamless frames. Therefore, the strength of the floor slabs must be checked for pushing under the loads from columns, bearing walls or stiffening diaphragms. The analysis of engineering solution of beamless monolithic reinforced concrete slabs of the administration nine-storey building with frame-walled load-bearing system is made. The strength thereof for pushing is found to be not provided under the given loads in a number of cases, due to this, experimental studies of strengthening the near-column areas of floor slabs have been carried out. When restoring the structures that suffered defects and damages in the course of their operation, composite materials having high tensile strength, low weight, constructibility and resistance to aggressive influence are widely used. The presented method for strengthening the near-column areas of floor slabs for ensuring their pushing strength with the use of chemical anchors has been developed, and a comparative analysis of the calculation results of the near-column areas of floor slabs with the adopted strengthening method with the results of experimental studies of slab fragments has been carried out. The operating conditions of the near-column areas of the floor slab have been simulated under the test method, and the results of the experimental samples testing are presented. All samples were found to have been destroyed by pushing through, with the destruction being of a plastic nature. The results of assessing the application of transverse reinforcement to the load-carrying capacity of the slab on pushing-through are presented. The results of experimental studies on assessing the pushing strength of extreme parts of monolithic floor slabs with columns reinforced with transverse glued-in reinforcement have shown good efficiency.