The objective of this paper is to investigate the effects of scale of an auxetic cellular material sample on the evaluation of elastic properties. Size and boundary effects are studied in detail. This is achieved by conducting computer simulations of the auxetic structure under the typical loading exerted by the compression and simple shearing test performed by means of ABAQUS FEA. The material microstructure is discretized by the plane network of Timoshenko beam elements. The results of the studies give insight to the scale effects. Structures with designed properties can be potentially used for engineering applications.