The tympanic membrane (TM), located at the end of the ear canal, is a collagenous multi-layer soft tissue membrane with fibers highly aligned in radial and circumferential orientations. This unique multi-layer fiber ultrastructure makes TM's mechanical behavior display both anisotropy and nonlinearity, which is important in sound transmission. However, the constitutive model of TM which includes both features has not been proposed. In this study, we develop a fiber-reinforced mesoscale constitutive model of TM which captures both anisotropic and nonlinear elastic mechanical behaviors. The TM is considered a continuum fiber-reinforced composite with two families of collagen fibers. Its overall properties are built up by integrating its heterogeneous material properties through the thickness. The homogenized mechanical properties are assumed to be uniformly distributed through TM's thickness and superposed by three uncoupled elastic contributions of radial collagen fibers, circumferential collagen fibers, and an equivalent isotropic matrix. The model is calibrated using literature data through the inverse method. Simulation results indicate that specific collagen fibers alignment is responsible for the significant spatial and directional variation of deformation of the TM strip. With the appropriate strength criteria related to fiber deformation, the anisotropic localized failure mode of the TM strip observed in the experiment can be captured. The nonlinear nature and rotation of collagen fiber bundles are the origin of the nonlinear mechanical behavior of TM strips under uniaxial loading. The mesoscale constitutive model offers a different perspective on TM's anisotropic and nonlinear elastic mechanical behavior. This research improves our understanding of the mechanical behavior of the TM and could help biomimetic graft development.