On the surface of structural elements during operation may appear various damages - notches, cavities, cuts, cracks. The presence of surface defects leads to an increase in stress values in their vicinity. In this regard, such surface defects can accelerate the failure of the structure. To estimate the stress values in the vicinity of local defects, the finite element method often used. In this paper we consider a thin-walled spherical shell, on the outer surface of which there are defects in the form of spherical notches. With the help of the ANSYS finite element package, the stress state is investigated. Calculations are made in the framework of the linear theory of elasticity.