The purpose of this paper is to investigate the effect of project risk on capital rationing with uncertain budgetary constraints. We reflect project risk by the standard deviation of cash flows. The problem is formulated in a stochastic linear programming with simple recourse (SLPSR) framework. In a sample problem, we vary the level of project risk and allow the probability distribution for the right-hand side constraints to be either symmetric or left skewed. We demonstrate that SLPSR yields superior solutions to an equivalent deterministic formulation and that risk aside, the borrowing rate is an important factor in determining the optimal solution vector. Moreover, we show that low project risk can compensate for higher borrowing costs and that the presence or absence of probability distribution asymmetry may not be an important issue.