This paper studies an optimal irreversible extraction problem of an exhaustible

commodity in presence of regime shifts. A company extracts a natural resource from a reserve

with finite capacity, and sells it in the market at a spot price that evolves according to a Brownian

motion with volatility modulated by a two state Markov chain. In this setting, the company

aims at finding the extraction rule that maximizes its expected, discounted net cash

flow. The problem is set up as a finite-fuel two-dimensional degenerate singular stochastic control problem

over an infinite time-horizon. We provide explicit expressions both for the value function and for

the optimal control. We show that the latter prescribes a Skorokhod reflection of the optimally

controlled state process at a certain state and price dependent threshold. This curve is given

in terms of the optimal stopping boundary of an auxiliary family of perpetual optimal selling

problems with regime switching. The techniques are those of stochastic calculus and stochastic

optimal control theory.