An introduction is given to the concept of a continuous Boltzmann machine (CBM) and an application to solve a class of partial differential equations (PDEs) is detailed. After briefly stating the problems, the BM is presented at a conceptual level. The basic ideas are taken to another level, and a fresh concept, CBM, is introduced, with the differences discussed in some detail. As Boltzmann machines have solved hard NP-complete optimization problems, the CBM has been used to solve large systems of elliptic PDEs arising in steady-state physical fields. Numerical results of simulations proved the characteristic features of the CBM.