This work is devoted to the research of the strength and elastic properties of the laminated fiberglass composite. Experiments were performed on tension and compression of specimens with different orientation of the reinforcement in relation to the loading direction. The predictions of three different failure criteria (Hill criterion, Tsai-Wu criterion, Zakharov criterion) were compared to experimental results. The strength and elastic properties of the composite separate components have been also researched with the aim to perfom finite element simulation of composite failure process. The elastic moduli of the composite are determined by means of the method of the finite element homogenization.