Auxetic structures exhibit certain abnormal mechanical behaviours such as negative Poisson's ratios, mainly through the intertwined deformation attributes of inter-connected members of macro structural forms. Auxetic tubular structures have been fabricated and studied due to their potential properties against tensile and pressure loads. In this thesis, different auxetic tubular structures which exhibit auxetic behavior in both compression and tension are investigated via finite element method. To validated finite element model, a test piece was fabricated and then tested by a tensil-comression machine. A comparision between expremental data and those obtaind from the finite element model show a good degree of agreement. Effect of different parameters such as void fraction and tubular thickness are examined on the value of force and Poisson ratio of auxetic tubular structures under compression and tension loads. Results show that by decreasing the void fraction and increasing the thickness of tubular under compression and tension loads, the energy absorption of structur will increase. Also, by increasing the void fraction and decreasing the thickness of tubular under compression and tension loads, an increase in negative Poisson's ratio will happen. Comparing different auxetic structures under compression loads show that re-entrant and one of the models with elliptic geometries has the maximum and the minimum energy absorption, respectively. Also, when tensile loads apply, S-shape structure exhibits the maximum energy absorption. The maximum and minimum negative Poisson's ratio are related to the S-shape and the re-entrant structures, respectively. Based on modal analysis it can be observed that via increasing the thickness of the tubular and also by decreasing the void fraction cause to increase the structure’s natural frequencies. However, the effect of thickness on increasing the natural frequency is not significant while a considerable effect was observed from void fraction. Also, comparing different auxetic structures show that the re-entrant and one of the models of elliptic geometries have the maximum and the minimum longitudinal frequency, respectively. Keywords: Auxetic structure; Negetive Poisson's ratio; Finite element method; Void fraction; Modal analysis.