There is a growing literature on the economics of aquaculture. Existing studies in this area may be categorized into two groups. The first focuses on aquaculture itself, including the analyses of production processes and the aquaculture product market. The second examines interactions between aquaculture and other activities, including the impacts of aquaculture on commercial fisheries and on the marine environment. We examine the interaction between a natural fishery and aquaculture using an economic optimal control model. The model is designed to determine the socially optimal scale of aquaculture in a region given that commercial fisheries already exist. In the model, a regional planner chooses both the optimal scale of aquaculture and fishing effort so that the net social benefit of fish production from both the commercial fishery and aquaculture is maximized. In the model, we examine two types of impacts of aquaculture on the fishery. First, the cost of fishing rises as aquaculture expands (e.g. due to interference with fishing operations). In addition, an expanding aquaculture area affects the carrying capacity of natural fish stocks. These are modeled as two constraints describing the dynamics of natural fish stock and aquaculture acreage, respectively. We develop two case studies. In the first case, ocean aquaculture produces the same species as the commercial fishery. In the second case, different species are produced by the fishery and aquaculture, and these products sold in different markets. Our model is an extension of a classical fishery bioeconomic model. It can be used to assess a number of important policy variables. For example, it may be used to examine the steady-state (long-run equilibrium) level of aquaculture with respect to different levels of impacts on the natural fish stock. Numerical examples are developed to illustrate the interactions between aquaculture and commercial fisheries and the optimal scale under various economic and biological conditions.