A detailed analysis of the nonthermal X-ray emission from the North-Western and Southern parts of the supernova remnant (SNR) HESS J1731$ - $347 with {\it Suzaku} is presented. The shell portions covered by the observations emit hard and line-less X-rays. The spectrum can be reproduced by a simple absorbed power-law model with a photon index $\Gamma$ of 1.8-2.7 and an absorption column density $N_{\rm H}$ of (1.0-2.1)$\times 10^{22}$ cm$^{-2}$. These quantities change significantly from region to region; the North-Western part of the SNR has the hardest and most absorbed spectrum. The Western part of the X-ray shell has a smaller curvature than North-Western and Southern shell segments. A comparison of the X-ray morphology to the Very High Energy (VHE) gamma-ray and radio images was performed. The efficiency of electron acceleration and emission mechanism in each portion of the shell are discussed. Thermal X-ray emission from the SNR was searched for but could not be detected at a significant level.