In this paper, we present a new model and two mechanisms for auctions in two-sided markets of buyers and sellers, where budget constraints are imposed on buyers. Our model incorporates polymatroidal environments, and is applicable to a wide variety of models that include multiunit auctions, matching markets and reservation exchange markets. Our mechanisms are build on polymatroidal network flow model by Lawler and Martel, and enjoy various nice properties such as incentive compatibility of buyers, individual rationality, pareto optimality, strong budget balance. The first mechanism is a simple "reduce-to-recover" algorithm that reduces the market to be one-sided, applies the polyhedral clinching auction by Goel et al, and lifts the resulting allocation to the original two-sided market via polymatroidal network flow. The second mechanism is a two-sided generalization of the polyhedral clinching auction, which improves the first mechanism in terms of the fairness of revenue sharing on sellers. Both mechanisms are implemented by polymatroid algorithms. We demonstrate how our framework is applied to internet display ad auctions.