In bank/trade credit financing, bank/supplier plays monitoring role and pays the fixed and variable monitoring costs. This study investigates the impact of monitoring cost on bank financing and trade credit financing in a push supply chain with a dominant supplier selling to a capital‐constrained retailer who can borrow competitively priced bank loans or trade credit. With a modified selling to the newsvendor Stackelberg game, we obtain the chain's equilibrium financing strategies. We find that bank financing is adopted only when the inefficient supplier sells to the very poor retailer. When the retailer is not very rich, the efficient supplier offers trade credit financing with trade credit rate equal to a risk‐free rate, even in the presence of supplier's monitoring cost, otherwise, the retailer uses either bank financing or self‐financing, depending on the retailer's initial capital and the bank's and the supplier's monitoring cost. There exists a chain efficiency loss region (supplier's monitoring distortion) that the poor retailer uses bank financing at the supplier's benefit, while the overall output can be improved through trade credit financing. The presence of the bank's monitoring cost might benefit the chain. When the factoring market is intensely competitive, we find that factoring can improve the channel efficiency and the supplier's profit. Through this study, we theoretically extend the delegated monitoring theory that the third‐party intermediated financing helps improve the channel performance.