In this paper, we study image block coding using the Boltzmann machines. We first briefly review the basic idea of storing images in the invariant distributions of the Markov chains, in particular, the Markov chains are the Boltzmann machines. Then we present the perfect Boltzmann machine (FBM) which can simulate any distributions. A FBM with n neurons has neural connections up to nth order. In practice, only the Boltzmann machines (second order) or third order Boltzmann machines are used. We discuss how to convert a FBM to a Boltzmann machine. Finally, we present the idea of image block coding using the Boltzmann machines. The idea is to represent images in terms of blocks in a similar way as JPEG. The DCT in JPEG is replaced by Boltzmann machine transformation. Image compression ratios for various selections of block size and parameter space are calculated.