The paper deals with the possible replacement of steel reinforcement by GFRP reinforcement for concrete elements subjected to bending moment and compressive axial force. For the last 15 years, Fibre Reinforced Polymer (FRP) bars became more popular and commercially available as reinforcement for concrete elements. Composite FRP materials are still new in construction and many engineers are not familiar with their properties and behaviour. FRP has certain advantages over steel reinforcement. It is a durable material that is not subject to corrosion, does not conduct heat, is an electrical insulator and conducts electrical current, and is non-magnetic. In contrast, FRP also has certain deficiencies such as sensitivity to higher temperatures, alkaline environments, and reduction of mechanical properties at high levels of long-term stress. In the case of FRP reinforcements, the plastic branch is missing in the σ-ε diagrams, what leads to a sudden failure of the reinforced concrete element, either by tensile rupture of the reinforcement or by crushing the concrete. The most used FRP reinforcement is made of glass fibres - GFRP reinforcement. The paper deals with the possible replacement of steel reinforcement by GFRP reinforcement for slab and beam elements. The text describes a parametric study for different reinforcement ratio with GFRP reinforcement and steel reinforcement. The study is performed for a cross-section of 500x500 mm for a column element and a cross-section of 1000x250 mm for a slab element. The effect of longitudinal GFRP reinforcement in elements under compression was investigated. The study contains a comparison of interaction P-M diagrams of concrete elements with steel and GFRP reinforcement. For design of GFRP reinforced concrete elements, it is necessary to consider different material characteristics such as tensile strength and modulus of elasticity. The contribution of the GFRP reinforcement in compression was neglected due to the anisotropic nature of the GFRP reinforcement and the low modulus of elasticity. The main reference basis for the elaboration of a parametric study is the fib Bulletin No. 40.