Packaging structures and methods for semiconductor devices are disclosed. In one embodiment, a substrate for packaging a semiconductor device includes a core substrate, an insulating material disposed over the core substrate, and conductive lines disposed in the insulating material. Contact pads are disposed over the insulating material and the conductive lines. The contact pads are disposed in an integrated circuit mounting region of the core substrate. A solder mask define (SMD) material is disposed over the insulating material. Portions of the contact pads are exposed through openings in the SMD material. A stress-relief structure (SRS) is disposed in the SMD material proximate the contact pads. The SRS is disposed entirely in the integrated circuit mounting region of the core substrate.