Antennas with radiation patterns conforming to a specified shape have many applications. Further, precise shaping of the main beam is often required. Array antennas are especially suited for shaped beam synthesis. The purpose of this thesis is to introduce an iterative technique for the shaped-beam synthesis of unequally spaced, nonuniformly excited linear arrays. The technique requires an initial approximation to the desired radiation pattern. This approximation may be attained by any classical synthesis method. Successive iterations are then applied to the initial pattern and are of two types, element current perturbations and element position perturbations. These two iteration types are applied in a variety of sequences and with different weighting functions. Several examples are considered for some typical radiation patterns. In one particular example of a sector pattern both the maximum main beam ripple and sidelobe level are reduced to approximately -40 dB using a 20-element array. Many comparisons are made and the effectiveness of the technique is evaluated. / Master of Science