Currently there are many applications for the use of composites reinforced with fiberglass mat and fabrics with polyester resin: automotive, aerospace, construction of wind turbines blades, sanitary ware, furniture, etc. The structures made of composites have a complex geometry, can be simultaneously subjected to tensile–compression, shear, bending and torsion. In this paper we analyzed the mechanical properties of a polyester composite material reinforced with glass fiber (denoted GFRP) of which were carried out two types of samples: The former contains four layers of plain fabric (GFRP-RT500) and the second type contains three layers of chopped strand mat (GFRP-MAT450). The samples were subjected to tensile, compression and tensile–tensile cyclic loading. The results highlight the differences between the two types of GFRP in terms of initial elastic modulus, post yield stiffness and viscoelastic behavior under cyclic loading. Thus, it was observed that the value of the modulus of elasticity and the value of ultimate tensile stress are approximately twice higher in the case of GFRP-RT500 than for the composite reinforced with short fibers type GFRP-MAT450. The tensile–tensile cyclic test highlights that the short glass fiber-reinforced composite broke after the first stress cycle, compared to the fabric-reinforced composite in which rupture occurred after 15 stress cycles. The elasticity modulus of GFRP-RT500 decreased by 13% for the applied loading with the speed of 1 mm/min and by 15% for a loading speed of 20 mm/min.