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Many animal connective tissues are composite materials formed into sheaths containing regularly organized collagen fibres in a crossed, fabric-like array. From a few simple assumption about the interactions between fibres, we construct a model for the effect of such a fabric-like construction on the Poisson's ratio of connective tissue sheaths. Surprisingly, the model predicts high Poisson's ratios (often greater than 1.0) Mdashespecially high given the value of 0.5 that is usually used for primarily aqueous biological tissues (based on assumptions of incompressibility and anisotropy). However, virtually all empirical attempts to measure Poisson's ratio in animal connective tissue sheaths (including our own experiments on salamander skin) reveal similarly high Poisson's ratios. The model also predicts that Poisson's ratio will increase with increasing strain, at a rate dependent on the initial angle of the crossed fibres relative to the direction of strain. Since the Poisson's ratio of a material is directly correlated with the material's stiffness, such strain-dependent changes in Poisson's ratio have important implications for the stiffness properties of connective tissue sheaths. Given the structural support role of connective tissues, stiffness is assumed to be one of their most important qualities, and several examples of how our model might predict the stiffness qualities within the walls of cylinders formed from helically wound crossed fibre sheaths (such as mammalian annular ligament and nematode cuticle) are given.