Microelectromechanical systems (MEMS) are typically 2D or quasi-3D structures fabricated using surface and bulk micromachining processes. In this work, an approach for 3D structure fabrication based on stress engineering is demonstrated. Specifically, sub-mm 3D spherical cage-like structures are realized through the deformation of bilayers of residually-stressed silicon oxide and silicon nitride with micrometer-scale thicknesses. Analytical and finite models to predict the shape of stress-engineered structures based on geometry and residual stress are described and used for structure design. A systematic experimental study was performed to quantify residual stresses in silicon nitride films made by plasma-enhanced chemical vapor deposition (PECVD). The measurements show that the residual stress of PECVD silicon nitride can be tuned over a wide range of tensile stresses through the control of deposition parameters, such as flow rate and power. Stress engineered 3D cage-like structures comprised of PECVD silicon nitride and oxide films were fabricated. 3D structures with a range of curvatures were demonstrated. The measured geometry of the fabricated structures are in good agreement with predictions from analytical and finite element models.