Composite structures during an operation are subjected to various types of external loading (impact, vibration, cyclic, etc.), which may lead to a decrease in mechanical properties. Previously, many experimental investigations of the mechanical behavior of composites under uniaxial cyclic loading were carried out. Acquisition of new data on the reduction of composite materials’ mechanical characteristics under conditions of multiaxial cyclic loading, as well as verification of existing models for calculation of the residual properties, are relevant. Therefore, this work is devoted to the experimental investigation of the mechanical behavior of fiberglass tubes under proportional cyclic loading. Static and fatigue tests were carried out under tension with torsion conditions. Inhomogeneous strain fields were obtained using a non-contact optical video system VIC-3D. The structural damage accumulation processes were analyzed by an AMSY-6 acoustic emission signals recording system. Surface defects were determined using a DinoLite microscope. Residual dynamic elastic modules were calculated during fatigue tests, and fatigue sensitivity curves were built. Data was approximated using various models, and their high descriptive capability was revealed. Damage accumulation stages were determined. The dependence of the models’ parameters on a stress state were observed. It was concluded that multiaxial cyclic loading leads to a significant decrease in mechanical properties, which should be taken into account in composite structure design.