The current literature on irreversible investment decisions usually makes the assumption of a constant interest rate. We study the impact of interest rate and revenue variability on the decision to carry out an irreversible investment project. Given the generality of the valuation problem considered, we first provide a thorough mathematical characterization of the two-dimensional optimal stopping problem and develop some new results. We establish that interest rate variability has a profound decelerating or accelerating impact on investment demand depending on whether the current interest rate is below or above the long run steady state interest rate, and that its quantitative size may be very large. Allowing for interest rate uncertainty is shown to decelerate rational investment demand by raising both the required exercise premium of the irreversible investment opportunity and the value of waiting. Finally, we demonstrate that increased revenue volatility strengthens the negative impact of interest rate uncertainty and vice versa.