We investigate the effect of fiber elongation on power loss as rays propagate along deformed polymer optical fibers (POFs). Variations in core diameter, incident angle, stress and strain distributions, and necking of the POFs during fiber elongation are studied. The power losses in the deformed POFs are analyzed both experimentally and numerically. Theoretical analysis based on an elastic-plastic finite-element model and a planar waveguide assumption is proposed. It is found that fiber elongation significantly affects the power loss in POFs, particularly at higher values of elongation. Good agreement between the measured results and the results simulated from the proposed model is obtained. The maximum difference is less than 5%. Results indicate that the proposed theoretical analysis based on an elastic-plastic finite-element model and a planar waveguide assumption is feasible to predict the power loss variation introduced by elongated deformations. A curve-fitted equation is also proposed to estimate the power loss of POFs under different fiber elongation conditions.