A modified vortex lattice method is developed to solve for the nonlinear three-dimensional unsteady incompressible flow over delta wings. Symmetric motions (pitching, heaving) and asymmetric motions (roll, yaw) are considered. Then the method is generalized to treat the nonlinear three-dimensional steady flow for bodies and wing body combinations. Numerical examples include variety of shapes and comparison with existing experimental data and other numerical methods over a wide range of angle of attack shows good agreement. For bodies alone the results deteriorate downstream of the separation region, while for wing-body combinations the agreement with the experimental data is good as long as the body separation effect is not large. The developed computer codes should provide a useful tool in the design of aircraft and missiles. / Ph. D.