An analysis of the single-fiber fragmentation test was investigated. An approximate solution for the stress fields of a fiber embedded in a polymer matrix of different elastic moduli was obtained by the Eshelby method. The fiber was modeled as a prolate spheroid. The axial stress of the fiber increases with increasing aspect ratio and fiber-matrix shear modulus ratio and decreases with increasing matrix and fiber Poisson's ratios. Using this analysis, the fracture stress of a single-fiber fragmentation specimen was derived. The applied stress at fiber fracture decreases monotonically with increasing aspect ratio of the fragmented fiber and increases with increasing fiber and matrix Poisson's ratios. This model is in qualitative agreement with published experimental data.