The design of the elliptical antenna arrays is relatively new research area in the antenna array community. Backtracking search optimisation algorithm (BSA) is employed for the synthesis of elliptical antenna arrays having different number of array elements. For this aim, BSA is used to calculate the optimum angular position and amplitude values of the array elements. BSA is a population-based iterative evolutionary algorithm. The remarkable properties of BSA are that it has a good optimisation performance, simple implementation structure, and few control parameters. The results of BSA are compared with those of self-adaptive differential evolution algorithm, firefly algorithm, biogeography based optimisation algorithm, and genetic algorithm. The results show that BSA can reach better solutions than the compared optimisation algorithms. Iterative performances of BSA are also compared with those of bacterial foraging algorithm and differential search algorithm.