Fiber irregularities are inherent to textile fibers, particularly natural fibers. This series of papers examines the impact of fiber irregularity on the mechanical behavior of textile fibers. Part I examines the effect of fiber dimensional irregularities on the tensile behavior of linear elastic fibers using the finite element method. Fiber dimensional irregularities are simulated with sine waves of different magnitude and frequency. The results indicate that increasing the level or magnitude of irregularity will decrease the breaking load, breaking elongation, and method Young's modulus of the fiber, while increasing the frequency of irregularity will decrease the breaking load and method Young's modulus, but the breaking elongation will increase. Fiber dimensional irregularity and the gauge length effect are also simulated in this study.