During tensile testing along the predominant fiber direction ligament and tendon tissue exhibit large Poisson’s ratios ranging from 1.3 in capsular ligament to 2.98 in flexor tendon. Although the microstructure of these tissues has been the topic of much investigation, the relationship between microstructure and Poisson’s ratio is relatively unexplored. A number of different microstructures have been suggested, which include models of fibril crimp and models that superimpose a macroscopic helical twist on top of fibril crimp. The aim of this study was to generate micromechanical models of the aforementioned microstructures in order to determine the influence of fibril organization on the effective Poisson’s ratio. Finite element models for each microstructure were constructed using solid hexahedral elements and featured 37 discrete fibrils embedded within a matrix. A convergence study was performed to determine the optimal mesh density. Both the fibril and matrix were modeled using a compressible Neo-Hookean material. Periodic boundary conditions were applied to all models and a uniaxial stress state was generated both parallel and perpendicular to the fiber direction. Using Hooks law the resulting stresses and strains allowed the determination of the effective Poisson’s ratio for each microstructure. A parametric analysis was performed in order to determine model sensitivity to the selection of material coefficients and geometric parameters. Results indicated that crimp alone was insufficient for generating large Poisson’s ratios. Adding a super-helical twist, however, was sufficient for generating large effective Poisson’s ratios. The sensitivity studies revealed a strong dependence on the selection of material coefficients. Models with a large ratio of fiber modulus to matrix modulus generated the largest Poisson’s ratios, as did models featuring a large ratio of fiber Poisson’s ratio to matrix Poisson’s ratio. Helical pitch also had a strong influence on the results, with a lower helical pitch (i.e. more twisting) generating the largest Poisson’s ratios. Based on the results of this study it is suggested that crimp alone is not sufficient in explaining the large Poisson’s ratios seen experimentally and that some other microstructure (such as a helical twist) is required.