The object of research is the design and stress–strain state of the precast concrete element’s rigid connection. For connection, composite rods are used, which are glued into prepared holes and channels. The reinforced concrete elements are connected by rods vertically and horizontally. In addition, for more uniform stresses transfer, polyurethane sheets are installed at the element’s joint. Method. To analyze the stress-strain state of the precast concrete element’s connection, a flat finite element model is used. The quadrangular physically non-linear finite elements are used for concrete modeling. For calculations, a non-linear stress-strain diagram for concrete, given in the regulatory documents for the reinforced concrete structures design, was applied. The deformation diagram of steel reinforcement is elastic-plastic. Composite rods are deforming elastically. The polyurethane sheets were modeled by nonlinear two-node finite elements working in compression and shear. Results. The quickly constructed structure for connecting precast concrete elements is proposed. A numerical analysis of the stress-strain state of such a connection is performed using the example of calculating the beam and the bridge arch. The comparison of the strength and rigidity of prefabricated and corresponding monolithic structures was made.