In this dissertation, we examine mechanics of rhythmic tracheal compression (RTC) in the darkling beetle, Zophobas morio. In Chapter 2, we studied the relationship between hemolymph pressure and tracheal collapse to test the hypothesis that pressure is a driving mechanism for RTC. We found that tracheae collapse as pressure increases, but other physiological factors in the body may be affecting tracheal compression in live beetles. Additionally, as the tracheae compress, they do so in varying spatial patterns across the insect body. In chapter 3, we examined spatial variations in the taenidial spacing, stiffness, and tracheal thickness along the length of the tracheae. We related variations in Young's modulus and taenidial spacing with measurements of collapse dimples and found that spatial patterns of Young's modulus correlate with dimensions of collapse dimples. This correlation suggests an intuitive link between tracheal stiffness variations and the unique patterns observed in compressing tracheae. Lastly, in chapter 4, we studied the non-uniform collapse patterns in 3-D. By manually pressurizing the hemocoel and imaging using synchrotron microcomputed tomography (SR-µCT), we reconstructed the tracheal system in its compressed state. While previous studies used 2-D x-ray images to examine collapse morphology, ours is the first to quantify collapse patterns in 3-D and compare with previous 2-D quantification methods. Our method is also the first to make a direct measure of tracheal volume as the tracheal system compresses, similar to the phenomenon that occurs during rhythmic tracheal compression. / Doctor of Philosophy / Insects have long been a source of curiosity and inspiration for scientists and engineers. The insect respiratory system stands as an example of a seemingly complex oxygen delivery system that operates with relative simplicity. As opposed to mammals and other vertebrates, the insect respiratory system does not deliver oxygen using blood. Instead, insects possess a massive network of hollow tracheal tubes that are distributed throughout the body. Air enters spiracular valves along the length of the insect body, travels through the tracheal tube network, and is delivered directly to the tissues. In some insects, the tracheae compress and expand, driving flow of respiratory gasses. However, unlike vertebrate lungs, there are no muscles directly associated with the tracheal system that would drive this tracheal compression, and exactly how this behavior occurs is not fully understood. In this dissertation, we examined pulsatory increases in blood pressure as a possible mechanism that underlies these tracheal compressions in the darkling beetle, Zophobas morio. Additionally, as the tracheae compress, they do so with varying spatial patterns across the insect body. Because tracheae are complex and non-uniform composite tubes, we examined spatial variations in the microstructure, stiffness, and tracheal thickness along the length of the trachea. Lastly, we visualized the variable collapse patterns in three dimensions using synchrotron micro-computed tomography combined with manual pressurization of the hemocoel. While previous studies used two-dimensional x-ray images to quantify tracheal collapse patterns, this work represents the first three-dimensional study. Understanding tracheal collapse mechanics, material properties, and their relationships with the circulatory system can help to gain an understanding of how insects create complex fluid flows within the body using relatively simple mechanisms.