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.