The polar-symmetric problem of thermoelasticity for a multilayer sphere is solved. Using this solution and based on the analogy between a libre thermal strain in an elastic body and a libre eigenstrain in a galvanic coating, the problem of determination of residual stresses (eigenstresses) in a multilayer galvanically grown sphere is solved. The compatibility problem of the solution is considered. As an example, residual stresses are determined for a coating on a thin-walled spherical substrate (application of equations (38) and (51) which modify the Mills method [7]).
