Methods and structures for forming strained-channel FETs are described. A strain-inducing layer may be formed under stress in a silicon-on-insulator substrate below the insulator. Stress-relief cuts may be formed in the strain-inducing layer to relieve stress in the strain-inducing layer. The relief of stress can impart strain to an adjacent semiconductor layer. Strained-channel, fully-depleted SOI FETs and strained-channel finFETs may be formed from the adjacent semiconductor layer. The amount and type of strain may be controlled by etch depths and geometries of the stress-relief cuts and choice of materials for the strain-inducing layer.