The thermal expansion mismatch of thermal grown silica on a silicon wafer is well known to induce compressive stress upon cooling from the growth temperature to room temperature. In this Letter, we investigate how this stress impacts silica disk structures by comparison of measurements with both a finite element and an analytical model. The disk structures studied are also whispering gallery optical resonators, and proper control of stress is critical to obtain high-Q resonances. Based on our analysis, thicker oxide layers and proper control of undercut enable ultra-high-Q optical performance and mechanical stability. (C) 2013 American Institute of Physics. [http://dx.doi.org/10.1063/1.4789370]