A giant single crystal of poly(trans-1,4-diethyl muconate), obtained from the single crystal of the corresponding monomer by photoinduced solid-state polymerization reaction, was put under tension along the chain axis and the infrared and Raman spectra were measured as a function of tensile stress. The bands of skeletal vibrational modes were found to shift toward lower frequency side with relatively large amount, while those of side group did not shift very much or shifted rather to higher frequency direction. These data were analyzed on the basis of normal-modes calculation under a quasi-harmonic approximation, allowing us to estimate the microscopic deformation mechanism of the polymer chain under tension. The Young's modulus along the chain direction was calculated to be 63.8 GPa at 0 K, corresponding relatively well to the experimental value 47.1 GPa obtained from the stress-strain curve measured for the polymer single crystal at room temperature.