Pipelines are structures of significant importance, so the demands for strength of the repair supplements is high. Methods of analysis of such pipeline-bandage systems are receiving considerable attention. The most common approach to the analysis of the pipeline with the installation of composite bandages is the use of the finite element method. Using commercial software packages enables the possibility to analyse the stress state, taking into account the geometry features of real defects and mechanical properties of composite materials and pipes. The current work focuses on the development of methods for the optimal parameters selection of composite bands, which are installed on the damaged sections of pipelines. Two optimization problems have been formulated in this investigation. The aim of the first is to provide equiresistant structure, so that repaired area’s maximum stress intensity would not be different from the intensity of the stresses on the undamaged sections of the pipeline. The aim of the second optimisation problem is to minimize the volume of the bandage with restriction that stress intensity on repaired area is smaller than on undamaged region.