Growth period models, previously treated in the literature, have assumed that the pattern of value increase of the growth asset is deterministic. In this paper, this assumption is relaxed by considering models in which the increase in value of an asset in a period is a random variable whose distribution is a function of either the value or the age of the asset at the start of the period. The expected increase in value is a decreasing function of the value or age of the asset so that the value of additional maturation time decreases as the asset ages. Dynamic programming is used to compute optimal policies as to when stochastic growth assets should be harvested. The steady state value function is shown to be directly analogous to that obtained when deterministic growth is assumed. Procedures for quickly computing both steady state policies and value functions are developed.