Plant layout is concerned with the spatial arrangement of processing equipment, storage vessels and their interconnecting pipework. This is an important aspect in the design of chemical and process plants since a good layout will ensure that the plant functions correctly and will provide an economically acceptable balance between the many, often conflicting, design constraints. These constraints are derived from safety, environmental, construction, maintenance and operational considerations. Process relationships, for example the use of gravity flow, and issues such as the provision of space for future expansion must also be taken into account. Traditional methods for locating equipment within chemical plants are based on mixtures of process heuristic rules and exact-to-the-inch distance information. Such techniques are unsystematic and they do not make use of all the relevant and appropriate data. In this paper an optimization based approach is used to determine a good preliminary plant layout, subject to all of the above constraints. A novel mathematical formulation is presented which addresses the problem of locating items of equipment within a given two or three dimensional space. The objective function to be minimised is the sum of the relevant operation, connection and floor construction costs. Detailed cost factors ate used to account for the flow direction between two connected units. The problem is formulated as a mixed integer linear programming problem. Specific attention is paid to constructing a formulation which is suitable for the solution of large scale problems. The method presents the rigorous solution of problems with around 30 process equipment and of essentially unlimited size problems when combined with single heuristic rules. The approach is demonstrated with several practical scale problems, including an industrial multi-purpose plant.