Abstract <p> The stress-strain state arising after a two-stage spherically symmetric process “radial loading– partial unloading” in a hollow sphere (thick-walled spherical layer) nonuniform in radius is investigated. The inner boundary is fixed, and a radial compressive stress is applied to the outer boundary. The material of the sphere agrees with Ilyushin’s theory of small elastoplastic deformations. Both discontinuous and continuously stratified nonuniformity are admitted, while the bulk modulus of compression at all points of the material is assumed to be constant. At the first (intermediate) step, an excessive compression (over-compression) occurs, as a result of which the radius of the outer boundary becomes less than the required one. At the second step, where partial unloading occurs, the system is transferred to the required final position. Such a two-stage nature enables one to control the stress-strain state in the hollow sphere both as a whole and concerning its individual parameters. </p> <p> <b> DOI</b> 10.1134/S1061920825030070 </p>