This article presents the results of a numerical study of the stress concentration around two equal and unequal holes in an orthotropic spherical shell made of composite materials under the action of internal pressure. The influence of geometric (hole radii, shell thickness, distance between holes) characteristics, as well as material orthotropy and shear stiffness, on the stress state of spherical shells made of composite materials is studied. A numerical algorithm based on the finite element method has been developed and a software package has been implemented on a computer that allows solving the problem of stress concentration near two unequal holes in spherical shells made of composite materials.