In this paper, the non-linear dynamic response of rectangular atomic force microscopy in tapping mode is considered. The effect of cantilever’s geometrical parameters (e.g., cantilever length, width, thickness, tip length and the angle between the cantilever and the sample's surface in liquid environment has been studied by taking into account the interaction forces. Results indicate that the resonant frequency, amplitude and phase are very sensitive to changes of geometrical parameters. In order to improve and optimize the system's behavior, the sensitive analysis (SA) of geometrical parameters on the first resonant frequency and amplitude of cantilever's vertical displacement has been conducted using Sobol's method. Results show that the influence of each geometrical variable on frequency response of the system can play a crucial role in designing the optimum cantilever in liquid medium for soft and sensitive biological samples. Also, one way to speed up the imaging process is to use short cantilevers. For short beams, the Timoshenko model seems to be more accurate compared to other models such as the Euler-Bernoulli. By using the Timoshenko beam model, the effects of rotational inertia and shear deformation are taken into consideration. In this paper, this model has been used to obtain more accurate results