The article discusses coatings of building structures in the form of shells, made of advanced composite materials. A mathematical shell model takes into account the geometric nonlinearity, orthotropy of material, transverse shifts, presence of reinforcement ribs. The study algorithm of this model is based on the minimization of the functional of the total potential energy of shell deformation and the linearization of the problem through best parameter continuation. Based on the software product developed, a comprehensive study of the strength and stability of various shell structures has been conducted. The efficiency of the use of orthotropic composite materials compared to traditional isotropic ones is shown.