In this paper, we consider the financial equilibrium problem consisting of multiple sectors, each of which seeks to determine the optimal size of its portfolio, along with its optimal holdings of assets as well as liabilities. We construct the network underlying each sector's optimization problem and then provide the equilibrium conditions and the equivalent variational inequality formulation. We identify the financial network that represents the system in equilibrium and propose the modified projection method for the computation of the equilibrium assets, liabilities, portfolio sizes, and prices. The algorithm decomposes the problem into network subproblems. We then provide numerical examples illustrating the model and the computational approach.