A nonlinear three-dimensional vortex-lattice method which treats the steady separated flow over prolate bodies with open separation moving through an inviscid incompressible fluid is developed. The strength and position of the body wake are found as part of the solution. Specifically, flows with smooth-surface separation are considered as opposed to flows with sharp-edge separation treated· with the vortex-lattice concept in the past. To demonstrate the technique, results for the flow over an inclinded ogive-cylinder are presented. In the case of attached flow, comparsions are presented of the results from the vortex-lattice method using optimal and average control point locations with the results of the source-distribution method and with experimental data. Significantly, the same panel arrangement is used in the calculations for both methods. The results demonstrate that the results of the present method is somewhat more sensitive to panel arrangement than are those of the source-distribution method. Also, the effect of control point location varies dramatically as the incidence of the body is changed. In the case of separated flow, comparsions of the results of the vortex-lattice method are made with experimental data and with the results of a typical two-dimensional analogy. The results demonstrate that the present method agrees most favorably with the experimental data windward of a separation line. / Doctor of Philosophy