Natural resource revenues provide a valuable source to finance public investment in developing countries, which frequently face borrowing constraints and tax mobilization problems. This paper develops a dynamic stochastic model to analyze the macroeconomic effects of investing resource revenues, making explicit the role of public investment inefficiency, absorptive capacity constraints, Dutch disease, and financing needs to sustain capital. Revenue exhaustibility raises medium-term issues of how to sustain capital built during a windfall, while revenue volatility raises short-term concerns about macroeconomic instability. Using the model, country applications show how combining public investment with a resource fund—a sustainable investing approach—can address the problems associated with exhaustibility and volatility. The applications also demonstrate how the model can be used to determine the appropriate magnitude of the investment scaling-up (accounting for the financing needs to sustain capital) and the adequate size of a stabilization fund (buffer).