The paper describes a study of the behaviour of eccentrically compressed cylindrical concrete elements strengthened with FRCM (Fabric Reinforced Cementitious Matrix), with PBO (p-Phenylene Benzobis Oxazole) mesh reinforcement - PBO-FRCM. The effect of concrete confinement on the mechanics of the strengthened eccentrically compressed elements was investigated. The load-bearing capacity, deformability, failure mechanisms and ductility of the tested elements were analysed. In addition to standard measurement methods, the tests were carried out used a digital image correlation system (DIC) to identify the stage of initiation and analyse the propagation of a crack at the end of PBO mesh, which announces the delamination of the overlap. Concrete with a compressive strength of approximately 45 MPa (typical for currently designed columns) was used in the study. The specimens were strengthened with 1, 2 or 3 layers of PBO mesh. The test elements were compressed either axially or eccentrically at two different eccentricities. The studies have shown that the dependence of the load-bearing capacity increase on the ratio of strengthening reinforcement in the presented studies is linear, and the obtained deformability and ductility of elements strengthened with 3 layers of PBO mesh are significantly higher compared to their counterparts with 1 and 2 layers of reinforcement (mainly in the case of axially compressed elements). The research carried out will be extended by numerical simulations to create a model for predicting the load-bearing capacity of eccentrically compressed reinforced concrete columns strengthened with PBO-FRCM composites.