Abstarct: In this thesis, vibration behavior and the sensivity of atomic force microscopy cantilever which is made of hyperelastic material have been analysised. The hyperelastic matreials are inherently nonlinear. The effects of various parameters such as the geometry of cantilever and tip, material of cantilever on the dynamic behavior of AFM microcantilever, and the frequency and sensivity of AFM microcantilever have been investigated and analysed. Because of the amplitude in contact mode is low, the interaction force between tip and sample surface is assumed linear. To get the governing equation, the Hamilton method is used. Strain energy is obtained from hyperlastric Yeo Model. Free vibration of the microcantileve is studied baxsed on Euler -Bernoulli's model with one clamped end and a mass and spring at another end. The effects of different parameters such as the number of modes, length, thickness, effective mass, length of the cone of the tip and the ratio of slenderness to the non-dimensional frequency are studied. In solving nonlinear equations, semi-analytic and approximate methods of Poincaré and Galerkin are used. Frequency and sensitivity values for Hyperlastric AFM microcantilever have increased significantly compared to the usual one. The vertical stiffness has a great influence on the frequency and AFM sensitivity. In the high vertical stiffness, no other geometric parameter changes would be effective. Up to now, no investigation is performed on the AFM with hyperelastic microbeam and the results of this thesis are the first results.