Silicon-based ultra-thin chips (UTCs) are used to build flexible system-in-foils (SiFs) for bio-sensing and biomonitoring, and utilize CMOS devices that deliver much higher performance than alternatives such as organic or thin-film transistors. Flexible SiFs experience significant mechanical stress in the field due to the deformation caused during daily use. These impact circuit performance, potentially causing a loss in functionality. This paper first models the stress due to two types of packages schemes for UTCs. Next, the stress is translated to shifts in mobility and threshold voltage of CMOS devices. Finally, the system-level performance variations of two common SiF elements, an A/D converter and an SRAM, are evaluated.