Photoacoustic imaging (PAI) is a non-invasive imaging modality that combines the absorption contrast of light with ultrasound resolution. Laser is used to deposit optical energy (i.e., optical fluence) into a target. As a result, the target temperature changes and causes thermal expansion to the target that leads to generating a PA signal. One of the important parameters that control the PA is the elasticity of the target. In general, most the PA studies and image reconstruction algorithms for PAI assumes isotropic elasticity within the target. However, it is known that certain soft tissues, like muscles and glands, are anisotropic with respect to elastic deformation. Also, observations indicate that breast tumors tend to be anisotropic. This could affect the reconstruction of PA images. In this study, we have investigated the influence of the anisotropic elasticity on PA back-propagation imaging using finite element method. The Fluence distribution was estimated by solving light propagation within a tissue model using Monte Carlo method. The results show that the object may appear in the reconstructed image about 10% larger or 12% smaller than the expected size based on the distribution of the young's modulus within the object if its anisotropic elasticity was not considered in the reconstruction algorithm.