The behaviour of the auxetic structure under external load was regarded as the behaviour of the compliant (flexible) mechanism. The multi-objective topological optimization, based on genetic algorithms and the finite element method, was used to find the optimal shape of such two-dimensional compliant mechanism in this study. The optimization was performed on a quarter of a double-symmetric representative unit cell, which is a building block of the symmetrical auxetic structure. Static linear computational simulations were performed to determine the mechanical response of cell topologies. The proposed method leads to a set of best solutions positioned on the Pareto front with different topologies and gives a broad overview of possible designs of new auxetic structures. The method is highly effective and can be easily extended to large deformation formulations, nonlinear elasticity or elasto-plasticity.