This paper presents mathematical programming models for the optimal process plant layout based on a continuous dimensional space. Two alternative formulations are proposed which can accommodate rectangular equipment footprints of arbitrary size. Then, one of the formulations is extended to account for a common designer objective : to organize the layout into well-defined production sections. All models are formulated as mixed-integer linear programming (MILP) problems which can be solved to global optimality by using commercial optimization software. The applicability of the proposed mathematical models is demonstrated by a number of illustrative examples.