Two financing modes are usually used to reduce the losses of the manufacturer as well as the supply chain’s profits resulted from the supplier’s capital constraints: one is equity financing mode, and the other is debt financing mode. We analyze the manufacturer’s optimal financing and the supplier’s optimal production decisions, and then compare the supply chain performances in these two modes. It is shown that the supplier must accept the debt financing, while the supplier will accept the equity financing only if some conditions are satisfied. Under equity financing mode, if the supplier’s initial capital is smaller than a critical value and the fraction of the supplier’s profit the manufacturer shares is higher than a critical value, the production at the capital-constrained supplier will be restored to the optimal level without capital constraints. Under debt financing mode, if the supplier’s initial capital is larger than a critical value, the production at the capital-constrained supplier will be restored to the optimal level without capital constraints. If the following strategy is used, performances of the manufacturer and supply chain will be optimal: when the supplier’s initial capital is small, the equity financing mode is used and fraction of the supplier’s profit the manufacturer shares is set to be high; on the contrary, when the supplier’s initial capital is large, the debt financing mode is used. Finally, the numerical study is given to demonstrate the conclusions.