This paper studies a version of the neoclassical growth model where heterogeneous establishments are subject to partial irreversibilities in investment. Under such investment technology, the optimal decision rules of establishments are of the (S,s) variety. A novel contribution of the paper is the analysis of the general equilibrium dynamics arising from aggregate productivity shocks. This is a difficult task given the high dimensionality of the state vector, which includes the distribution of establishments across capital levels and idiosyncratic shocks. The paper overcomes this difficulty by developing a suitable computational approach. The model is used to study the importance of investment irreversibilities for macroeconomic dynamics. It is found that investment irreversibilities have no major implications for aggregate fluctuations, even though they are crucial for establishment level dynamics. This result contradicts previous conclusions in the literature which rely on partial equilibrium analysis.